TY  - BOOK
AU  - Lasiecka,I.
TI  - Mathematical control theory of coupled PDEs
T2  - CBMS-NSF regional conference series in applied mathematics
SN  - 0898714869
AV  - QA402.3 .L333 2002
U1  - 629.8312 21
PY  - 2002///]
CY  - Philadelphia
PB  - Society for Industrial and Applied Mathematics
KW  - Control theory
KW  - Differential equations, Hyperbolic
KW  - Differential equations, Parabolic
KW  - Coupled mode theory
N1  - Includes bibliographical references (pages 225-238) and index; Preface --; 1; Introduction --; 1.1; Control Theory of Dynamical PDEs --; 1.1.1; Finite- versus infinite-dimensional control theory --; 1.1.2; Boundary/point control problems for single PDEs --; 1.1.3; Boundary/point control problems for systems of coupled PDEs --; 1.2; Goal of the Lectures --; 2; Well-Posedness of Second-Order Nonlinear Equations with Boundary Damping --; 2.1; Orientation --; 2.2; Abstract Model --; 2.3; Existence and Uniqueness: Statement of Main Results --; 2.4; Nonlinear Plates: von Karman Equations --; 2.4.1; Case [gamma] > 0 --; 2.4.2; Case [gamma] = 0 --; 2.5; Semilinear Wave Equation --; 2.6; Nonlinear Structural Acoustic Model --; 2.7; Full von Karman Systems --; 2.7.1; Model --; 2.7.2; Formulation of the results: Case [gamma] = 0 --; 2.7.3; Formulation of the results: Case [gamma] > 0 --; 2.8; Comments and Open Problems --; 3; Uniform Stabilizability of Nonlinear Waves and Plates --; 3.1; Orientation --; 3.2; Abstract Stabilization Inequalities --; 3.3; Semilinear Wave Equation with Nonlinear Boundary Damping --; 3.3.1; Formulation of the results --; 3.3.2; Regularization --; 3.3.3; Preliminary PDE inequalities --; 3.3.4; Absorption of the lower-order terms --; 3.3.5; Completion of the proof of the main theorem --; 3.4; Nonlinear Plate Equations --; 3.4.1; Modified von Karman equations --; 3.4.2; Full von Karman system and dynamic system of elasticity --; 3.4.3; Nonlinear plates with thermoelasticity --; 3.5; Comments and Open Problems --; 4; Uniform Stability of Structural Acoustic Models --; 4.1; Orientation --; 4.2; Internal Damping on the Wall --; 4.3; Boundary Damping on the Wall --; 4.3.1; Model --; 4.3.2; Formulation of the results --; 4.3.3; Preliminary multipliers estimates --; 4.3.4; Microanalysis estimate for the traces of solutions of Euler-Bernoulli equations and wave equations --; 4.3.5; Observability estimates for the structural acoustic problem --; 4.3.6; Completion of the proof of Theorem 4.3.1 --; 4.4; Thermal Damping --; 4.4.1; Model --; 4.4.2; Statement of main results --; 4.4.3; Sharp trace regularity results --; 4.4.4; Uniform stabilization: Proof of Theorem 4.4.2 --; 4.4.5; Wave equation --; 4.4.6; Uniform stability analysis for the coupled system --; 4.5; Comments and Open Problems --; 5; Structural Acoustic Control Problems: Semigroup and PDE Models --; 5.1; Orientation --; 5.2; Abstract Setting: Semigroup Formulation --; 5.3; PDE Models Illustrating the Abstract Wall Equation (5.2.2) --; 5.3.1; Plates and beams: Flat[Gamma subscript 0] --; 5.3.2; "Undamped" boundary conditions: g [identical with] 0 in (5.3.10) --; 5.3.3; Boundary feedback: Case g [not equal] 0 in (5.3.10) and related stability --; 5.3.4; Shells: Curved-wall [Gamma subscript 0] --; 5.4; Stability in Linear Structural Acoustic Models --; 5.4.1; Internal damping on the wall --; 5.4.2; Boundary damping on the wall --; 5.5; Comments and Open Problems --; 6; Feedback Noise Control in Structural Acoustic Models: Finite Horizon Problems --; 6.1; Orientation --; 6.2; Optimal Control Problem --; 6.3; Formulation of the Results --; 6.3.1; Hyperbolic-parabolic coupling --; 6.3.2; Hyperbolic-hyperbolic coupling: General case --; 6.3.3; Hyperbolic-hyperbolic coupling: Special case of the Kirchhoff plate with point control --; 6.4; Abstract Optimal Control Problem: General Theory --; 6.4.1; Formulation of the abstract control problem --; 6.4.2; Characterization of the optimal control --; 6.4.3; Additional properties under the hyperbolic regularity assumption --; 6.4.4; DRE, feedback generator, and regularity of the gains B*P, B*r --; 6.5; Riccati Equations Subject to the Singular Estimate for e[superscript At]B --; 6.5.1; Formulation of the results --; 6.5.2; Proof of Lemma 6.5.1 --; 6.5.3; Proof of Theorem 6.5.1 --; 6.6; Back to Structural Acoustic Problems: Proofs of Theorems 6.3.1 and 6.3.2 --; 6.6.1; Verification of Assumption (6.4.1) --; 6.6.2; Verification of Assumption 6.5.1 --; 6.7; Comments and Open Problems --; 7; Feedback Noise Control in Structural Acoustic Models: Infinite Horizon Problems --; 7.1; Orientation --; 7.2; Optimal Control Problem --; 7.3; Formulation of the Results --; 7.3.1; Hyperbolic-parabolic coupling --; 7.3.2; Hyperbolic-hyperbolic coupling: Abstract results --; 7.3.3; Hyperbolic-hyperbolic coupling: Kirchhoff plate with point control --; 7.4; Abstract Optimal Control Problem: General Theory --; 7.4.1; Formulation of the abstract control problem --; 7.4.2; ARE subject to condition (7.4.15) --; 7.5; ARE Subject to a Singular Estimate for e[superscript At]B --; 7.5.1; Formulation of the results --; 7.5.2; Proof of Theorem 7.5.1 --; 7.6; Back to Structural Acoustic Problems: Proofs of Theorems 7.3.1 and 7.3.2 --; 7.7; Comments and Open Problems --; Bibliography --; Index
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