Roberto Triggiani

Professor Emeritus

Research Areas
Control Theory, Partial Differential Equations
Publications/Research

Books Published

Differential and Algebraic Riccati Equations with applications to boundary/point control problems: Continuous theory and approximation theory (with I. Lasiecka), Vol. 164, Springer-Verlag Lecture Notes Series in Control and Information Sciences, 1991, 160 pp.

Research monographs: Control Theory for Partial Differential Equations: Continuous and Approximation Theories, Vol. 1 (680 pp.), and Vol. 2 (422 pp.) (with I. Lasiecka), Encyclopedia of Mathematics and Its Applications Series, Cambridge University Press, January 2000 (Vol. 3 in preparation, 6 chapters completed.) It contains numerous new results by the authors not appeared in print before. Both volumes received the Featured Review by the AMS.

Tangential Boundary Stabilization of Navier–Stokes Equations (with V. Barbu and I. Lasiecka), Memoirs AMS 181 (852) (May 2006), 28 pp.

Nonlinear exact controllability and nonlinear stabilization of hyperbolic or hyperbolic-like evolution equations, Matematica Contemporanea, 38 (2010), 192 pp. Outgrowth of lectures given at Universidade Federal do Rio de Janeiro, August 3–7, 2009.

Boundary Control and Boundary Inverse Theory for Non-Homogeneous Second-Order Hyperbolic Equations: A Common Carleman Estimates Approach (with S. Liu), to be published under SISSA auspices in a book series of the American Institute of Mathematics in 2012, 110 pp. [Outgrowth of lectures given at SISSA (Scuola Internazionale di Studi Avanzati), Trieste, Italy, May 2011.]

Research monograph: Stabilization and controllability of nonlinear control systems governed by partial differential equations (with I. Lasiecka), in preparation, preliminary draft of 450 pages available, Springer-Verlag.

Editor of Control Problems for systems described by partial differential equations and applications (with I. Lasiecka), Springer-Verlag Lecture Notes 97. Proceedings of the IFIP-WG 7.2 Working Conference held at University of Florida, Gainsville, 1986, pp. 396.

Editor of Differential geometric methods in the control of partial differential equations (with R. Gulliver and W. Littman) Contemporary Mathematics, Vol. 268 (2000), AMS Publication. Proceedings of AMSIMS-SIAM Summer Research Conference, held at the University of Colorado, Boulder, June 27–July 2, 1999.

Editor of Control Theory for Partial Differential Equations (with G. Leugering, O. Imannvilov, B. Zhang), CRC formerly Marcel Dekker Lecture Notes in Pure and Applied Mathematics, May 2005. Proceedings of NSF-supported Conference, held at Georgetown University, June 2004.

Editor of Control Methods in PDE-Dynamical Systems (with F. Ancona, I. Lasiecka, W. Littman), Contemporary Mathematics, expected to be published in 2006, AMS Publication. Proceedings of AMS-IMSSIAM Summer Research Conference, held at Snowbird Resort, Utah, July 2–7, 2005.

Refereed Journal Publications

Delayed control action controllable systems in Banach space, Control and Cybernetics, Polish Academy of Science 3 (1974), 95-117.

Controllability and observability in Banach space with bounded operators, SIAM J. Control Optimiz. 13(1) (1975), 462-49.

Pathological asymptotic behavior of control systems in Banach space, J. Math. Anal. Appl. 49 (1975),411-4

On the lack of exact controllability for mild solutions in Banach space, J. Math. Anal. Appl. 50(1975), 438-446.

Extensions of rank conditions for controllability and observability to Banach spaces and unbounded operators, SIAM J. Control Optimiz.14 (1976), 313-338.

On the stabilizability problem in Banach space, J. Math. Anal. Appl. 52 (1975), 383-403. Addendum: On the stabilizability problem. . ., J. Math. Anal. Appl. 56 (1976), 492-493.

A note on the lack of exact controllability for mild solutions in Banach Space, SIAM J. Control Optimiz. 15(3) (1977), 407-411.

Function space controllability of linear retarded systems: A derivation from abstract operator conditions (with A. Manitius), SIAM J. Control Optimiz. 16 (1978), 599-645.

Sufficient conditions for function space controllability and feedback stabilizability of linear retarded system (with A. Manitius), IEEE Transaction of Automatic Control, (1978), 659-665. (Also, announcement in Proceedings of the Decision and Control Conference, Florida, December 1976.

On the relationship between first and second order controllable systems in Banach space, SIAM J. Control Optimiz. 16 (1978), 847-859. (Also, preliminary versions in Proceedings of the International Workshop on Infinite Dimensional Systems, University of Rome, Italy, June 1976, Springer-Verlag Lecture Notes, and Proceedings of 1976 Allerton Conference on System Theory, University of Illinois, Urbana.)

A cosine operator approach to modeling boundary inputs problems for hyperbolic systems, Proceedings of 8th IFIP Conference on Differential Equations and Optimization Techniques, University of Wurzburg, West Germany, September 1977. Springer-Verlag Lecture Notes on Control Sciences 6 (1978), 380-390.

Analytic properties of cosine operators (with S. Nelson). Proceedings Amer. Math. Soc. 74 (1978),101-104.

Boundary stabilization of parabolic equations, International Conference on Recent Advances in Differential Equations, Miramare-Trieste (Italy), R. Conti (editor), Academic Press, August 1978. (Also, Proceedings of International Conference on Systems Analysis, I.R.I.A., Paris, Springer-Verlag LNCIS 14 (1978), 305-313.)

On Nambu's boundary stabilizability problem for diffusion processes, J. Diff. Eqns. 33 (1979), 189-200.

Well-posedness and regularity of boundary feedback parabolic systems, J. Diff. Eqns. 36 (1980),347-362.

Boundary feedback stabilizability of parabolic equations, Appl. Math. Optimiz. 6 (1980), 201-220.

A cosine operator approach to modelling L2 (0, T;L2(Ω)) boundary input hyperbolic equations (with I. Lasiecka), Appl. Math. Optimiz. 7 (1981), 35-83.

Hyperbolic equations with Dirichlet boundary feedback via position vector: Regularity and almost periodic stabilization, Part I (with I. Lasiecka), Appl. Math. Optimiz. 8 (1981), 1-37.

Hyperbolic equations with Dirichlet boundary feedback via position vector: regularity and almost periodic stabilization, Part II (with I. Lasiecka), Appl. Math. Optimiz. 8 (1982), 103-130.

Hyperbolic equations with Dirichlet boundary feedback via position vector: regularity and almost periodic stabilization, Part III (with I. Lasiecka), Appl. Math. Optimiz. 8 (1982), 199-221.

Structural assignment of Neumann boundary feedback parabolic equations: The case of trace in the feedback loop (with I. Lasiecka), Annali Matem. Pura Appl. (IV) XXXII (1982), 131-175.

An L2-theory for the quadratic optimal cost problem of hyperbolic equations with control in the Dirichlet B.C. (with I. Lasiecka), Springer-Verlag Lecture Notes 54 (1982), 138-153.

Stabilization and structural assignment of Dirichlet boundary feedback parabolic equations (with I. Lasiecka), SIAM J. Control Optimiz. 21 (1983), 766-803.

Dirichlet boundary control problem for parabolic equation with quadratic cost: Analyticity and Riccati'-s feedback synthesis (with I. Lasiecka), SIAM J. Control Optimiz. 21 (1983), 41-67.

Stabilization of Neumann boundary feedback parabolic equations: The case of trace in the feedback loop (with I. Lasiecka), Appl. Math. Optimiz. 10 (1983), 307-350. (Preliminary version in Springer-Verlag Lecture Notes 54 (1983), 238-246.)

Boundary feedback stabilization problems for hyperbolic equations, Springer-Verlag Lecture Notes 54 (1983), 238-246.

Feedback semigroups and cosine operators for boundary feedback parabolic and hyperbolic equations (with I. Lasiecka), J. Diff. Eqns. 47 (1983), 246-272.

Dirichlet boundary stabilization of the wave equation with damping feedback of finite range (with I. Lasiecka), J. Math. Anal. Appl. 97 (1983), 112-130.

Regularity of hyperbolic equations under L2 (0, T;L2(Γ))-Dirichlet boundary terms (with I. Lasiecka), Appl. Math. Optimiz. 10 (1983), 275-286.

Nondissipative boundary stabilization of hyperbolic equations with boundary observation (with I. Lasiecka), J. Math. Pures Appl. 63, (1984), 59-80.

A-bounded, finite rank perturbations of s.c. group generators A: Counterexamples to generation and another condition for well posedness. Springer-Verlag Lecture Notes in Mathematics(1984), 227-233. Proceedings of Workshop on Operator-Semigroups and Applications, University of Graz, Retzholf (Austria) June 1983.

Finite rank, relatively bounded perturbations of C0-semigroups, Part I: Well posedness and boundary feedback hyperbolic dynamics (with I. Lasiecka), Annali Scuola Normale Superiore di Pisa (IV) XII(4)(1985), 641-668.

Improving stability properties of hyperbolic damped equations by boundary feedback,Springer-Verlag Lecture Notes75 (1985), 400-409. Proceedings of Workshop on Control Theory for Partial Differential Equations and Applications, University of Graz (Austria), July 1984. (Also, Proceedings of CDC Conference, held in Las Vegas, December 1984.)

Finite rank, relatively bounded perturbations ofC0-semigroups, Part II: Spectrum allocation and Riesz basis in parabolic and hyperbolic feedback systems (with I. Lasiecka), Annali Matem. Pura Appl. (IV) CXLIII (1986), 47-100.

Riccati equations for hyperbolic partial differential equations with L2(Σ)-Dirichlet boundary terms(with I. Lasiecka), SIAM J. Control Optimiz. 24 (1986), 884-926.

Non homogeneous boundary value problems for second order hyperbolic operators (with I. Lasiecka and J. L. Lions), J. Math. Pures Appl. 65 (1986), 149-192.

A direct study of Riccati equations arising in boundary control problems for hyperbolic equations (with G. Da Prato and I. Lasiecka), J. Diff. Eqns. 64 (1986), 26-47.

Exponential uniform energy decay rates of the wave equation in a bounded region with L2 (0, T;L2(Γ)-boundary feedback in the Dirichlet B.C. (with I. Lasiecka), J. Diff. Eqns. 66 (1987), 340-390.

The regulator problem for parabolic equations with Dirichlet boundary control, Part I: Riccati'-s feedback synthesis, and regularity of optimal solutions (with I. Lasiecka), Appl. Math. Optimiz. 16(1987), 147-168.

The regulator problem for parabolic equations with Dirichlet boundary control, Part II: Galerkin approximation (with I. Lasiecka), Appl. Math. Optimiz. 16 (1987), 187-216.

Exact boundary controllability of L2(Ω)×H−1(Ω) of the wave equation with Dirichlet boundary control acting on a portion of the boundary and related problems, Appl. Math. Optimiz. 18(1988), 241-277. (Also, preliminary version in Springer-Verlag Lecture Notes 102 (1987), 291-332; Proceedings of Workshop on Control for Distributed Parameter Systems, University of Graz, Austria (July 1986)).

Proof of two conjectures of G. Chen and D. L. Russell on structural damping for elastic systems: The case α= 1/2 (with S. Chen), Springer- Verlag Lecture Notes in Mathematics 1354 (1988), 234-256. Proceedings of Seminar on Approximation and Optimization, University of Havana, Cuba (January 1987).

A lifting theorem for the time regularity of solutions to abstract equations with unbounded operators and applications to hyperbolic equations (with I. Lasiecka), Proceedings American Mathematical Society 103 (1988), 745-755.

Algebraic Riccati Equations with non-smoothing observation arising in hyperbolic and Euler-Bernoulli boundary control problems (with F. Flandoli and I. Lasiecka), Annali Matem. Pura Appl.(IV) CLM (1988), 307-382. (Preliminary version in Infinite Horizon Quadratic Cost Boundary Control Problems (with I. Lasiecka), Proceedings, CDC Conference, Los Angeles, CA, December 1987).

Exact controllability of the Euler-Bernoulli equation with L2(Σ)-control only in the Dirichlet boundary condition (with I. Lasiecka), Rendiconti Accademia Nazionale dei Lincei, Rome, Italy, Classe Sci. Fis. Matem. LXXXI (1988).

Wave equation on a bounded domain with boundary dissipation: An operator approach, J. Math. Anal. Appl. 137 (1989) 438-461. (Also, preliminary versions in Operator Methods for Optimal Control Problems, Sung J. Lee (editor), Marcel Dekker (1988), pp. 283; Lecture Notes Pure Appl. Math. 108, 283-310; Proceedings of Special Session of the Annual Meeting of the American Mathematical Society, New Orleans, LA (1986)).

Exact boundary controllability for the wave equation with Neumann boundary control (with I. Lasiecka), Appl. Math. Optimiz. 19 (1989), 243-290. (Also, preliminary version in Springer-Verlag Lecture Notes 100 (1987), 316-371.)

Trace regularity of the solutions of the wave equation with homogeneous Neumann boundary conditions and compactly supported data (with I. Lasiecka), J. Math. Anal. Appl. 141 (1989), 49-71.

Proof of extensions of two conjectures on structural damping for elastic systems: The case 1/2≤α≤1 (with S. Chen),Pacific J. Math. 136 (1989), 15-55.

Exact controllability of the Euler-Bernoulli equation with controls in the Dirichlet and Neumannboundary conditions: A non-conservative case (with I. Lasiecka),SIAM J. Control Optimiz.27(1989), 330-373. (Also, preliminary version in Semigroups and Applications, Marcel Dekker Lecture Notes116 (1988), 241-261.)

Regularity theory for a class of nonhomogeneous Euler-Bernoulli equations: A cosine operator ap-proach (with I. Lasiecka), Bollettino Unione Matem. Ital.(7)3-B (1989), 199-228. (Also, invitedpaper for special volume,Topics in Mathematical Analysis, volume dedicated to A. L. Cauchy,T. M. Rassias (editor), World Scientific (1989), 623-657).

Lack of uniform stabilization for non-contractive semigroups under compact perturbation,ProceedingsAmer. Math. Soc.105 (1989), 375-383.

Exact controllability for wave and Euler-Bernoulli equations in the presence of damping, 30 Yearsof Modern Optimal Control, Lecture Notes Pure Appl. Math. 119 (1989) 377-387, Marcel Dekker.(Also,Diff. Eqns. Appl.III (1989), 454-463, Ohio University Press.)

Exact controllability of the Euler-Bernoulli equation with boundary controls for displacement andmoment (with I. Lasiecka), J. Math. Anal. Appl.146 (1990), 1-33. (Also, invited paper for specialvolume,Topics in Mathematical Analysis, volume dedicated to A. L. Cauchy, T. M. Rassias (editor), World Scientific (1989), 576-622).

Finite rank, relatively bounded perturbations of semi-group generators, Part III: A sharp result onthe lack of uniform stabilization,Diff. Int. Eqns.3 (1990), 503-522. (Also, preliminary version in Proceedings INRIA Conference, Paris, France (June 1988), Springer-Verlag Lecture Notes.)

Sharp regularity for mixed second order hyperbolic equations of Neumann type Part I: TheL2-boundary case (with I. Lasiecka),Annali Matem. Pura Appl.(IV) CLVII (1990) 285-367. (An-nouncements in Accad. Lincei, LXXXIII (1989), 109-113, Classe di Scienze Matematiche, Rome, Italy, and Springer-Verlag Lecture Notes, 114.)

Gevrey class semigroups arising from elastic systems with gentle perturbation (with S. Chen),Proceedings Amer. Math. Soc.110 (1990), 401-415.

Characterization of domains of fractional powers of certain operators arising in elastic systems, andapplications (with S. Chen),J. Diff. Eqns. 88 (1990), 279-293.

Further results on exact controllability of the Euler-Bernoulli equation with control in the Dirich-let/Neumann boundary conditions (with I. Lasiecka), Springer-Verlag Lecture Notes, LNCIS147 (1990), 226-235, J. P. Zolesio (editor).

Exact controllability of semi-linear abstract systems with application to wave and plate problems(with I. Lasiecka), Appl. Math. Optimiz., 23 (1991), 109-154.

Uniform energy decay rates for Euler-Bernoulli equations with feedback operators in the Dirich-let/Neumann B.C. (with J. Bartolomeo),SIAM J. Math. Anal.22 (1991), 46-71. (Announcement in Rendiconti Accademia Nazionale dei Lincei, Rome, Italy,Classe Sci. Fis. Matem.(8) LXXXIII(1989), 121-128.)

Regularity theory of hyperbolic equations with non-homogeneous Neumann boundary conditions, Part II: General boundary data (with I. Lasiecka), J. Diff. Eqns. 94 (1991), 112-164.

Uniform stabilization of the Euler-Bernoulli equation with feedback only in the Neumann boundary conditions (with N. Ourada), Diff. Int. Eqns. 4 (1991), 277-292.

Regularity of structurally damped systems with point/boundary control, J. Math. Anal. Appl. 161(2)(1991), 299-331.

Numerical approximations of algebraic Riccati equations for abstract systems modelled by analytic semigroups, and applications (with I. Lasiecka), Math. Computation 57(196) (1991), 639-662 and Supplement 513-537.

Exact controllability and uniform stabilization of Euler-Bernoulli equations with only one active control in ∆w|Σ, (with I. Lasiecka), Bollettino Unione Matem. Ital. (7)5-B (1991), 665-702. (Also, invited paper for special volume dedicated to C. Caratheodory, T. M. Rassias (editor), World Scientific.)

Differential Riccati equations with unbounded coefficients: applications to boundary control/boundary observation hyperbolic problem (with I. Lasiecka), J. Nonlinear Anal. 17(7) (1991), 655-682. (Also, invited paper for special volume dedicated to E. F. Gauss, T. M. Rassias (editor), World Scientific 9.)

Exact controllability and uniform stabilization of Kirchhoff plates with boundary controls only in ∆w|Σ (with I. Lasiecka), J. Diff. Eqns. 93 (1991), 62-101. (Preliminary version in -Semigroup and Evolution Equations,- Marcel Dekker Lectures Notes Pure Appl. Math. 135, 267-295.)

Lack of exact controllability for wave and plate equations with finitely many boundary controls, Diff. Int. Eqns. 4 (1991) 683-705.

Riccati differential equations with unbounded coefficients and non-smoothing terminal condition: The case of analytic semigroup (with I. Lasiecka), SIAM J. Math. Anal. 25 (1992), 449-481.

Uniform stabilization of the wave equation with Dirichlet or Neumann-feedback control without geometrical conditions (with I. Lasiecka), Appl. Math. Optimiz. 25 (1992), 189-224. (Preliminary version in Springer-Verlag Lecture Notes LNCIS 147, 62-108, J. P. Zolesio (editor).)

Optimal regularity, exact controllability and uniform stabilization of the Schr-odinger equation (with I. Lasiecka), Diff. Int. Eqns. 5 (1992), 521-535.

Constructive steering control functions for linear systems and abstract rank conditions, J. Optimiz. Theory Appl. 74(2) (August 1992), 347-367.

Counterexamples to some stability questions for dissipative generators, J. Math. Anal. Appl. 170 (1992), 49-64.

Regularity with point control. Part III: Schrodinger equations, J. Math. Anal. Appl. 171 (1992), 567-577.

Uniform Convergence of Solutions to Riccati equations arising in boundary/point control problems (with I. Lasiecka), Springer Verlag Lecture Notes LNCIS 184 (1992), 285-305.

Interior and boundary regularity of the wave equations with point control, Diff. Int. Eqns. 6 (1993), 111-129. (Announcement in Accademia Nazionale dei Lincei, Rome, Italy, Matem. Appl. II(4) (1991), 307-315.)

Interior regularity with point control: Euler-Bernoulli equations, Springer Verlag Lecture Notes LNCIS 79, 321-355, J. P. Zolesio (editor).

Regularity with point control. Part II: Kirchhoff equations, J. Diff. Eqns. 103 (1993), 394-420.

Algebraic Riccati Equations arising from systems with unbounded input solution operator: Applications to boundary control problems for wave and plate problems (with I. Lasiecka), J. Nonlinear Anal. 20 (1993), 659-695. (Prelimary version in Springer-Verlag Lecture Notes LNCIS 180, 530-538. Proceedings of EFIP Conference, held in Zurich, Sept. 2-5, 1991.)

Sharp trace estimates of solutions to Kirchhoff and Euler-Bernoulli equations (with I. Lasiecka), Appl. Math. Optimiz. 28, (1993), 277-306. (Preliminary version in Marcel Dekker Lectures Notes Pure Appl. Math. 148. Proceedings of International Conference of Evolution Equations in Banach Space, held at University of Bologna, Italy (July 1991), 141-180.)

Analytic and Gevrey class semigroups generated by −A + iB, and applications (with A. Favini) Marcel Dekker Lectures Notes Pure Appl. Math. 148 (1993). Proceedings of International Conference on Evolution Equations in Banach Space, held at University of Bologna, Italy, July 1991, 148 (August 1993), 93-114. (Announcement appeared in Accademia Nazionale dei Lincei, Rome, Italy, Sezione Matematica, 1992).

Min-Max game theory and algebraic Riccati equations for boundary control problems with continuous input-solution map. Part I: The stable case (with C. McMillan), Marcel Dekker Lectures Notes Pure Appl. Math. 155 (1994). Proceedings of International Conference/Workshop in Evolution Equations in Banach Space, held in Han-sur-Lesse, Belgium, October 1991, Ph. Clement and G. Lumer (editors), 372-405.

Min-Max game theory and algebraic Riccati equations for boundary control problems with continuous input-solution map, Part II: The general case (with C. McMillan), Appl. Math. Optimiz. 29 (1994), 1-64. (Announcement appeared in Differential Equations with Applications to Mathematical Physics, Academic Press (1992), 239-49 and in Springer-Verlag LNICS.

Min-Max game theory and algebraic Riccati equations for boundary control problems with analytic semigroups, Part I: The stable case (with C. McMillan), Marcel Dekker Lecture Notes Pure Appl. Math. 152 (1994), 757-780, invited paper for special volume (Festschrift), in honor of L. Markus on the occasion of his 70th birthday.

Min-Max game theory and algebraic Riccati equations for boundary control problems with analytic semigroups. Part II: The general case (with C. McMillan), J. Nonlinear Anal. 22 (1994) 431-465.

An optimal quadratic boundary control problem for wave and plate-like equations with high internal damping: An abstract approach, Marcel Dekker Lecture Notes Pure Appl. Math. 165 (1994), 215-271. International Conference on Optimal Control for Partial Differential Equations, University of Trento, January 1993.

Lack of generation of strongly continuous semigroups by the damped wave operator on H - H (with A. V. Balakrishnan), Appl. Math. Letters 6 (1993), 33-37.

Optimal boundary control and new Riccati equations for highly damped second order equations, Diff Int. Eqns. 7 (1994), 1109-1144. Invited paper for special volume in memory of Peter Hess.

Further regularity properties of the optimal pair in quadratic cost problems for parabolic equations with boundary control and non-smoothing final state penalization (with I. Lasiecka), Marcel Dekker Lectures Notes Pure Appl. Math. 160 (1994), 173-190. International Conference on Optimal Control of Differential Equations and Calculus of Variations, Ohio University, March 1993.

On the relationship between the optimal control quadratic problem on an infinite horizon and on a finite horizon with final state penalization: The abstract hyperbolic case, Marcel Dekker Lectures Notes Pure Appl. Math. 160 (1994), 301-325. International Conference on Optimal Control of Differential Equations and Calculus of Variations, Ohio University, March 1993.

A sharp result on the exponential operator-norm decay of a family of s.c. semigroups, Semigroup Forum 49 (1994), 387-395.

Abstract model and semigroup well-posedness of spherical shells with boundary dissipation (with I. Lasiecka), invited paper in Dynamical Sys. Appl. 4 (1995), 453-471, World Scientific Series in Applicable Analysis.

Uniform stabilization of spherical shells by boundary dissipation (with I. Lasiecka and V. Valente), Advances Diff. Eqns. 1 (1996) 635-674. (Also, preliminary version in Marcel Dekker Lectures Notes Pure Appl. Math. 176 (1996), 171-181.

Carleman estimates and uniqueness for the system of strongly coupled PDE-s of spherical shells (with I. Lasiecka), special volume of Zeits. Angerwandte Math. Mech. (ZAMM), Akademie Verlag, Berlin, ICIAM 1995, 76(4) (1996), 277-280.

Regularity theory, exact controllability and optimal quadratic cost problem for spherical shells with physical boundary controls, invited paper in special issue of Control and Cybernetics, Polish Academy of Sciences, Control Problems Part. Diff. Eqns. 259(3) (1996), 553-569.

A singular control approach to highly damped second order abstract equations and applications (with I. Lasiecka and L. Pandolfi), Appl. Math. Optimiz. 36 (1997), 67-107. (Also, preliminary version in Marcel Dekker Lectures Notes Pure Appl. Math. 176 (1996), 157-170. Proceeding of Conference on Control of Partial Differential Equations, Laredo, Spain, September 1994.)

An optimal control problem with unbounded control operator and unbounded observation operator where the Algebraic Riccati Equation is satisfied as a Lyapunov equation, Appl. Math. Letters 10 (1997), 95-102.

Carleman estimates and exact boundary controllability for a system of coupled, nonconservative second order hyperbolic equations (with I. Lasiecka), Marcel Dekker Lectures Notes Pure Appl. Math. 188 (1997), 215-245, invited paper for the special volume Partial Differential Equations Methods in Control and Shape Analysis.

Carleman estimates and exact boundary controllability for a system of coupled non-conservative Schr-odinger equations, invited paper for special volume of Rendiconti dell- Istituto di Matematica dell- Universita di Trieste XXVIII (1996), 453-504. Supplemento, invited paper for special volume in memory of Pierre Grisvard.

An abstract setting for differential Riccati equations in optimal control problems for hyperbolic/Petrowski-type PDE-s with boundary control and slightly smoothing observation, Abstract Appl. Anal. 1 (1996), 435-484.

Exact controllability for second-order hyperbolic equations with variable coefficients-principal part and first-order terms (with I. Lasiecka and P. F. Yao), Non-Linear Anal. Theory Meth. Appl. 30 (1997), 111-122.

Analyticity, and lack thereof, of semigroups arising from thermo-elastic plates, special volume Computational Science for the 21st Century, John Wiley (1997), invited paper for a conference in honor of R. Glowinski, May 1997.

Analyticity, and lack thereof, of thermo-elastic semigroups (with I. Lasiecka), European Soc. Appl. Math. (ESAIM) 4 (1999), 199-222.

The Algebraic Riccati equation with unbounded control operator: The abstract hyperbolic case revisited, American Mathematical Society, Contemporary Mathematics, special volume Optimization Methods in Partial Differential Equations 209 (1997), 315-338.

Control problems in noise reduction: the case of two hyperbolic equations, Math. Contr. Smart Structures, SPIE 3039 (1997), 382-392.

Two direct proofs on the analyticity of the s.c. semigroup arising in abstract thermo-elastic equations (with I. Lasiecka), Advances Diff. Eqns. 3(3) (May 1998), 387-416.

Spectral analysis of thermo-elastic plates with rotational forces (with S. K. Chang), in Optimal Control: Theory, Algorithms, and Applications, Kluwer (1998), 84-115.

Exact null controllability of structurally damped and thermo-elastic parabolic models, (with I. Lasiecka), invited paper (Memoria), Accademia Nazionale dei Lincei, Mathematics Section, Rome, Italy, IX(1) (1998), 43-69.

Analyticity of thermo-elastic semigroups with coupled hinged/ Neumann B.C. (with I. Lasiecka), Abstract Appl. Anal. 3(1-2) (1998), 153-169.

Analyticity of thermo-elastic semigroups with free B.C. (with I. Lasiecka), Annali Scuola Normale Superiore, Pisa, Cl. Sci. (4), XXVII (1998), 457-482.

Sharp regularity of a coupled system of a wave and a Kirchoff equation with point control arising in noise reduction (with M. Camurdan), Diff. Int. Eqns. 12(1) (January 1999), 101-118.

High level interior and boundary regularity results of the Euler-Bernoulli equation with application to Differential Riccati Equations in optimal control, Numer. Funct. Anal. Optimiz. 20(3&4) (1999), 367-386.

Sharp regularity theory for thermo-elastic mixed problems, Applicable Analysis 77(3-4) (2001), 419-433. [Reprint of an electronically faulty version in 73(3-4) (1999), 557-572.]

A sharp trace result on a thermo-elastic plate equation with coupled hinged/Neumann boundary conditions (with I. Lasiecka), Discrete Cont. Dynam. Sys. 5 (July 1999), 585-598.

Finite element compensators for thermo-elastic systems with boundary control and point observation (with S. K. Chang and I. Lasiecka), Num. Funct. Anal. Optimiz. 20(5&6) (1999), 419-435.(117) Uniform stability of non-linear thermo-elastic plates with free boundary conditions (with G. Avalos and I. Lasiecka), International Series of Numerical Mathematics, Birkh-auser 133 (1999), 13-32.

An observability estimate in L2(Ω) - H−1 (Ω) for second order hyperbolic equations with variable coefficients (with I. Lasiecka and P. F. Yao), Control of Distributed Parameter and Stochastic Systems, Kluwer (1999), 71-79, S. Chen, X. Li, J. Yong, and X. Zhou (editors).

Inverse observability estimates for second order hyperbolic equations with variable coefficients (with I. Lasiecka and P. F. Yao), J. Math. Anal. Appl. 235 (July 1999), 13-57.

Inverse/observability estimates for Schr-odinger equations with variable coefficients (with P. F. Yao), invited paper, special volume on Control of Partial Differential Equations, Polish Academy of Sciences 28(3) (1999), 627-664.

Exact boundary controllability of a first order non-linear hyperbolic equation with non-local integral term arising in epidemic modeling (with I. Lasiecka), Direct and Inverse Problems of Mathematical Physics, R. P. Gilbert, J. Kajiwara, Y. Xu (editors), Kluwer (2000), 363-398. ISAAC-97, The First International Congress of the International Society for Analysis, its Applications and Computations.

Structural decomposition of thermo-elastic semigroups with rotational forces (with I. Lasiecka), Semigroup Forum 60 (2000), 16-66.

Feedback noise control in an acoustic chamber: Mathematical theory (with I. Lasiecka), Nonlinear Problems in Aviation and Aerospace, Gordon and Breach Science Publishers (2000), 89-111. S. Siva (editor), Vol. 11, Stability and Control: Theory Methods and Applications, 1999.

Extended algebraic Riccati equations in the abstract hyperbolic case (with V. Barbu and I. Lasiecka), Nonlinear Anal. 40(1-8) (2000), 105-130, Elsevier, invited paper for special issue in honor of Lakshmikantham.

Nonconservative wave equations with unobserved Neumann B.C.: Global uniqueness and observability (with I. Lasiecka and X. Zhang), AMS Contemp. Math., Vol. 268 (2000), 227-326.

Simultaneous exact/approximate boundary controllability of thermoelastic plates with variable thermal coefficient and moment control (with M. Eller and I. Lasiecka), J. Math. Anal. Appl. 251 (2000), 452-478.

A sharp trace regularity result of Kirchof and thermo-elastic plate equations with free boundary conditions (with I. Lasiecka), Rocky Mount. J. Math. 30(3) (2000), 981-1023.

Factor spaces and implications on Kirchoff elastic and thermoelastic systems with clamped boundary conditions (with I. Lasiecka), Abstract & Appl. Analysis, Vol. 6(8) (2001), 1-48. Preliminary announcement in Oberwolfach Proceedings -Control of Complex Systems, Kluwer.

Sharp regularity of the second time derivative wtt of solutions to Kirchhoff elastic equations with clamped boundary conditions (with I. Lasiecka), Int. J. Appl. Math. 11(44) (2001), 753-773.

Simultaneous exact/approximate boundary controllability of thermoelastic plates with variable coefficient (with M. Eller and I. Lasiecka), Marcel Dekker Lecture Notes Pure and Applied Mathematics 216 (February 2001), 109-230, invited paper for the special volume entitled Shape Optimization and Optimal Designs, J. P. Zolesio (Editor). [Preliminary version, is in invited paper in Semigroup of Operators and Applications, Birkhauser (2000), 335-351, A. V. Balakrishnan (editor).]

Backward uniqueness for thermoelastic plates (with I. Lasiecka and M. Renardy), Semigroup Forum 62 (2001), 217-242.

Simultaneous exact/approximate boundary controllability of thermoelastic plates with variable thermal coefficient and clamped controls (with M. Eller and I. Lasiecka), Discrete Cont. Dynam. Sys. 7(2) (2001), 283-301.

Unique continuation for over-determined Kirchoff plate equations and related thermoelastic systems (with M. Eller and I. Lasiecka), J. Inv. Ill-Posed Prob. 9(2) (2001), 1-46.

Optimal control and algebraic Riccati equations under singular estimates for e AtB in the absence of analyticity. Part I: The stable case (with I. Lasiecka), Marcel Dekker, Lecture Notes in Pure and Applied Mathematics, Vol. 225 (2002), 193-219, S. Aizicovici & N. Pavel (Editors).

Min-max game theory and optimal control with indefinite cost under a singular estimate for e AtB in the absence of analyticity, invited paper in memory of B. Terreni, Evolution Equations, Semigroups and Functional Analysis, Birkh-auser (2002), 353-380, A. Lorenzi & B. Ruf (Editors).

Singular estimates and uniform stability of systems of coupled hyperbolic/parabolic PDEs (with F. Bucci, I. Lasiecka), Abstract and Applied Analysis, Vol. 7(4) (2002), 169-237.

Uniform stabilization of a shallow shell model with nonlinear boundary feedback (with I. Lasiecka), J. Anal. & Appl., Vol. 269(2) (2002), 642-688.

Carleman estimates with no lower order terms for general Riemannian wave equations. Global uniqueness and observability in one shot (with P. F. Yao), Appl. Math. & Optimiz. 46(2-3) (2002), 331-375.

Carleman estimates for a plate equation on a Riemannian manifold with energy level terms (with I. Lasiecka and P. F. Yao), Analysis and Applications, Kluwer (2003), 199-236. H. Begehr, R. Gilbert, and M. W. Wang (Editors).

Optimal estimates of norms of fast controls in exact null controllability of two non-classical abstract parabolic systems, Advances in Diff. Eqns., Vol. 8(2) (2003), 189-229.

The coupled PDE system of a composite (sandwich) beam, Discr. & Contin. Dynam. Systems B, Vol. 3(2) (2003), 285-298.

The case for differential geometry in the control of single and coupled PDEs: The structural acoustic chamber (with R. Gulliver, I. Lasiecka, and W. Littman). IMA Volumes in Mathematics and its Applications, volume 137: Geometric Methods in Inverse Problems and PDE Control, Springer Verlag (2003), 73-181.

L2(Σ)-regularity of the boundary → boundary operator B∗L for hyperbolic and Petrowski PDEs (with I. Lasiecka), Abstract & Applied Analysis, Vol. 19 (2003), 1061-1139.

Global uniqueness, observability and stabilization of non-conservative Schr-odinger equations via pointwise Carleman estimates. Part I: H1 (Ω)-estimates (with I. Lasiecka and X. Zhang), J. Inverse & Ill-Posed Problems, Vol. 12(1) (2004), 1-81.

Global uniqueness, observability and stabilization of non-conservative Schr-odinger equations via pointwise Carleman estimates. Part II: L2(Ω)-estimates (with I. Lasiecka and X. Zhang), J. Inverse & Ill-Posed Problems, Vol. 12(2) (2004), 182-231. Preliminary announcement in Analysis and Optimization of Differential Systems, Kluwer (2003), 235-246.

Backward uniqueness of semigroups arising in coupled PDE systems of structural acoustics, Advances in Diff. Eqns., Vol. 8(1-2) (Jan.-Feb. 2004), 53-84. Preliminary announcement in Semigroups of Operators: Theory and Applications (2002), 285-300. C. Kubrusly, N. Levan, M. da Silveira (editors).

Optimal control and differential Riccati equations under singular estimates for e AtB in the absence of analyticity (with I. Lasiecka). Invited paper in honor of A. V. Balakrishnan, Advances in Dynamics and Control, Chapman and Hall/CRC (2004), Chapter 19, 271-307.

Internal stabilization of Navier-Stokes equations with finitely many controllers (with V. Barbu), Indiana Univ. Math. J. 53(5) (2004), 1443-1494.

The operator B∗L for the wave equation with Dirichlet control (with I. Lasiecka), Abstract and Applied Analysis, Vol. 2004, Issue 7, 625-634.

The dual algebraic Riccati equations: Additional results under isomorphism of the Riccati operator, Appl. Math. Letters 18 (2005), 1001-1008.

Global exact controllability on H1 Γ0 (Ω) - L2(Ω) of semilinear wave equations with Neumann L2(0, T;L2(Γ1))-boundary control, Control Theory for Partial Differential Equations, CRC Lecture Notes in Pure & Applied Mathematics, Vol. 242, Chapter 19, 271-334, May 2005.

Global exact controllability of semilinear wave equations by a double compactness/uniqueness argument (with I. Lasiecka), Discrete & Continuous Dynamical Systems, Supplement Volume (June 2005), 556-565.

Boundary stabilization of Navier-Stokes equations (with V. Barbu and I. Lasiecka), Memoirs AMS, 128 pp., Vol. 181, N. 852, May (2006).

Abstract settings for tangential boundary stabilization of Navier-Stokes equations by high- and lowgain feedback controllers (with V. Barbu and I. Lasiecka), Nonlinear Analysis 64(12) (June 2006), 2705-2746.

Well-posedness and uniform decay rates at the L2(Ω)-level of Schr-odinger equations with nonlinear boundary dissipation (with I. Lasiecka), J. Evol. Eqns. 6 (2006), 485-537.

Stability enhancement of a 2-D linearized Navier-Stokes channel flow by finite-dimensional, wallnormal boundary controllers, with arbitrarily small support, 39 pp., Discrete & Continuous Dynamical Systems B, 8(2) (2007), 279-314.

Pointwise Carleman estimates, global uniqueness, observability and stabilization for non-conservative Schr-odinger equations on Riemannian manifolds at the H1 (Ω)-level (with X. Xu), AMS Contemporary Math. 426 (March 2007), 339-404.

Sharp regularity of hyperbolic-dominated thermoelastic systems with point control: The hinged case, J. Math. Anal. & Appl., 333 (2007), 530-542.

The coupled PDE-system arising in fluid-structure interaction. Part I: Explicit semigroup generator and its spectral properties (with G. Avalos), AMS Contemporary Mathematics, Fluids and Waves 440 (2007), 15-55.

Sharp regularity of hyperbolic-dominated thermoelastic systems with point control: The clamped case, Discr. & Cont. Dynam. Systems 2007 (special) (September 2007), 993-1004.

Local exponential stabilization strategies of the Navier-Stokes equations, d = 2, 3, via feedback stabilization of its linearization (with V. Barbu and I. Lasiecka), Optimal Control of Coupled Systems of Partial Differential Equations, Oberwolfach, Birkhauser ISNM 155 (2007), 13-46.

Exact controllability in L2(Ω) of the Schr-odinger equation in a Riemannian manifold with L2(Σ1)-Neumann boundary control (invited paper) in: Functional Analysis and Evolution Equations (2008), 613-636. Special volume dedicated to the memory of G-unter Lumer; H. Amann, W. Arendt, J. von Below, M. Hieber, F. Neubrander, and S. Nicaise, editors, Birkh-auser Verlag.

The role of an L2(Ω)-energy level estimate in the theories of uniform stabilization and exact controllability for Schr-odinger equations with Neumann boundary control, Bol. Soc. Paran. Math. 25(1-2) (2007), 109-138. Invited paper, Inter. Conference on PDEs, State University of Maringa, Brazil, September 2007.

Mathematical analysis of PDE systems which govern fluid-structure interaction (with G. Avalos), Bol. Soc. Paran. Math. 25(1-2) (2007), 109-138. Invited paper, Inter. Conference on PDEs, State University of Maringa, Brazil, September 2007.

The critical case of clamped thermoelastic systems with interior point control: Optimal interior and boundary regularity results, J. Diff. Eqns. 245(12) (2008), 3764-3805.

Uniform stabilization of a coupled PDE system arising in fluid-structure interaction with boundary dissipation at the interface (with G. Avalos), Discr. & Cont. Dynam. Systems, 22(4) (2008), 817-833 (invited paper).

Backward uniqueness of the s.c. semigroup arising in parabolic-hyperbolic fluid-structure interaction (with G. Avalos), J. Diff. Eqns. 245 (3) (2008), 737-761.

Higher regularity of a coupled parabolic-hyperbolic fluid-structure interactive system (with G. Avalos and I. Lasiecka), invited paper, special issue of Georgian Mathematical Journal 15(3) (2008), 403-437; dedicated to the memory of J. L. Lions; J. Mawhin, editor.

Linear hyperbolic and Petrowski-type PDEs with continuous boundary control → boundary observation open loop map: Implications on nonlinear boundary stabilization with optimal decay rates (with I. Lasiecka), 187-276. Invited paper in Sobolev Spaces in Mathematics: Applications of Functional Analysis in Mathematical Physics, International Mathematical Series, Vol. 8, Springer Verlag (2008), dedicated to the centenary of Sergey Sobolev.

Uniform energy decay rates of hyperbolic equations with nonlinear boundary and interior dissipation (with I. Lasiecka), invited paper for special issue C&C, Control Journal of Polish Academy of Sciences in honor of J. P. Zolesio, 37(4) (2008), 932-966.

Linear independence of boundary traces of eigenfunctions of elliptic and Stokes Operators and applications, invited paper for special issue, Applicationes Mathematicae 35(4) (2008), 481-512, Institute of Mathematics, Polish Academy of Sciences.

Semigroup well-posedness in the energy space of a parabolic-hyperbolic coupled Stokes-Lam-e PDE system (with G. Avalos), Discr. & Cont. Dynam. Systems DCDS-S 2(3) (2009), 417-448.

Boundary feedback stabilization of a coupled parabolic-hyperbolic Stokes-Lam-e PDE system (with G. Avalos), J. Evol. Eqns. 9 (2009), 341-370. (174) Unique continuation from an arbitrary interior subdomain of the variable-coefficient Oseen equation, Nonlinear Analysis, Theory, Meth. & Appl. 17 (2009), 4967-4976.

Beyond lack of compactness and lack of stability of a coupled parabolic-hyperbolic fluid-structure system (with G. Avalos and I. Lasiecka), International Series of Numerical Mathematics, Vol. 158, Birkh-auser Verlag, Basel, Switzerland (2009), pp. 1-33 (Oberwolfach Conference).

Unique continuation of boundary over-determined Stokes and Oseen eigenproblems, Discr. & Cont. Dynam. Systems, DCDS-S (invited paper) 2(3) (2009), 645-678.

Optimal regularity and optimal control of thermoelastic structural acoustic model with point control and clamped boundary conditions (with C. Lebiedzik), 41 pages, invited paper, special issue C&C, Control Journal of Polish Academy of Sciences entitled, -50 Years of Optimal Control Theory,- Part B, 38 (2009), 1461-1500.

Min-max game theory and non-standard differential Riccati equations under singular estimates for e AtB and e AtG in the absence of analyticity (with J. Zhang), Set-Valued and Variational Analysis, Springer-Verlag, Vol. 17 (2009), 245-283.

A coupled parabolic-hyperbolic Stokes-Lam-e PDE system: Limit behavior of the resolvent operator on the imaginary axis (with G. Avalos), Applicable Analysis, Vol. 88(9) (2009), 1357-1396.

Backward uniqueness of the C0-semigroup associated with a parabolic-hyperbolic coupled StokesLam-e PDE system (with G. Avalos), Trans. Amer. Math. Soc. 362 (2010), 3535-3561.

A hidden gain of regularity on the strongly damped abstract wave equation: Implications on the nonlinear model, invited paper in Advances in Theory, Methods and Applications in Dynamics and Control, Chapter 8, a felicitation volume in honor of A. V. Balakrishnan, Cambridge (2011), 97-106.

The optimal interior regularity for the critical case of a clamped thermoelastic system with point control revisited (with C. Lebiedzik), modern Aspects of the Theory of PDEs. Vol. 216 of Operator Theory: Advances and Applications, 243-259, Birkh-auser/Springer, Basel, 2011. M. Ruzhansky and J. Wirth, eds.

A fluid structure interaction model with both control and disturbance at the interface: A game theory problem via an abstract approach (with I. Lasiecka and J. Zhang), Applicable Analysis, special issue, 90(5-6) (May-June 2011), 961-999.

Global uniqueness and stability in determining the damping coefficient of an inverse hyperbolic problem with non-homogeneous Neumann B.C. through an additional Dirichlet boundary trace (with S. Liu), SIAM J. Math. Analysis, 43(4) (2011), 1631-1666.

Min-max game theory and nonstandard differential Riccati equations for abstract hyperbolic-like equations, J. Nonlinear Analysis, Series A, special issue, 75 (2012), 1572-1591.

Global uniqueness and stability in determining the damping and potential coefficients of an inverse hyperbolic problem (with S. Liu), Nonlinear Analysis, Series B 12 (2011), 1562-1590.

Global uniqueness in determining electric potentials for a system of strongly coupled Schr-odinger equations with magnetic potential terms (with S. Liu), J. Inverse Ill-Posed Prob., 25 pp., 9(2) (June 2011), 223-254.

Recovery of damping coefficients for a system of coupled wave equations: Uniqueness and stability (with S. Liu), Chinese Annals Math., Series B, 35 pp., 32(5) (Sept. 2011), 669-698.

Determining damping and potential coefficients of an inverse problem for a system of two coupled hyperbolic equations. Part I: Global uniqueness (with S. Liu), Discr. & Cont. Dynam. Sys., suppl. (2011), 1001-1014.

An abstract semigroup approach to the third-order Moore-Gibson-Thompson PDE-equation arising in high-intensity ultrasound: Structural decomposition, spectral analysis, exponential stability (with R. Marchand and T. McDevitt), Math. Methods in Appl. Science 35 (2012), 1896-1929, invited paper, special issue in honor of R. Gilbert-s 80th birthday.

Global uniqueness and stability in determining the damping coefficient of an inverse hyperbolic problem with non-homogeneous Dirichlet BC, through an additional localized Neumann boundary trace (with S. Liu), Applicable Analysis 91(8) (2012), 1551-1581, invited paper, special issue on Direct & Inverse Problems for PDEs.

Recovering damping and potential coefficients for an inverse non-homogeneous econd-order hyperbolic problem via a localized Neumann boundary trace, invited paper for special issue of Discr. & Cont. Dynamical Systems, in honor of J. Goldstein, Discrete Contin. Dyn. Sysy. 33 (2013), 5217-5252.

An inverse problem for a third order PDE arising in high-intensity ultrasound: Global uniqueness and stability by one boundary measurement (with S. Liu), Journal of Inverse and Ill-Posed Problems 21 (2013), 825-869. Invited paper for a special issue dedicated to academician M. M. Levrentiev.

Rational decay rates for a PDE heat-structure interaction: A frequency domain approach (with G. Avalos), Evolution Equations and Control Theory 2 (2013), 233-253.

Min-max game theory and nonstandard differential Riccati equations for abstract hyperbolic-like equations. Nonlinear Anal. 75 (2012), no. 3, 1572–1591.

Fluid-structure interaction with and without internal dissipation of the structure: a contrast study in stability (with G. Avalos). Evol. Equ. Control Theory 2 (2013), no. 4, 563–598.

Creative/Artistic Works

Algebraic Riccati equations arising in boundary/point control: a review of the theoretical and numerical results: Part 1: continuous case (with I. Lasiecka), Perspectives in Control Theory, Birkhäuser (1990), 175–210.

Algebraic Riccati equations arising in boundary/point control: A review of the theoretical and numerical results: Part II: Approximation theory (with I. Lasiecka), Perspectives in Control Theory, Birkhäuser (1990), 210–235.

Recent advances in regularity of second-order hyperbolic mixed problems, and applications (with I. Lasiecka), invited paper for Book Series, Dynamics Reported, Springer-Verlag, 3 (1994), 104–158.

Min-max game theory and H∞-problems for partial differential equations with boundary/point control and disturbance. INRIA-IFIP Conference, held at Universite de Technologie de Compiegne, France, July 1993, Springer-Verlag Lecture Notes 197 (1994), 70–89.