Mathematical control theory of coupled PDEs /
Lasiecka, I. 1948-
Mathematical control theory of coupled PDEs / Irena Lasiecka. - xii, 242 pages ; 25 cm. - CBMS-NSF regional conference series in applied mathematics ; 75 . - CBMS-NSF regional conference series in applied mathematics ; 75. .
Includes bibliographical references (pages 225-238) and index.
Preface -- Introduction -- Control Theory of Dynamical PDEs -- Finite- versus infinite-dimensional control theory -- Boundary/point control problems for single PDEs -- Boundary/point control problems for systems of coupled PDEs -- Goal of the Lectures -- Well-Posedness of Second-Order Nonlinear Equations with Boundary Damping -- Orientation -- Abstract Model -- Existence and Uniqueness: Statement of Main Results -- Nonlinear Plates: von Karman Equations -- Case [gamma] > 0 -- Case [gamma] = 0 -- Semilinear Wave Equation -- Nonlinear Structural Acoustic Model -- Full von Karman Systems -- Model -- Formulation of the results: Case [gamma] = 0 -- Formulation of the results: Case [gamma] > 0 -- Comments and Open Problems -- Uniform Stabilizability of Nonlinear Waves and Plates -- Orientation -- Abstract Stabilization Inequalities -- Semilinear Wave Equation with Nonlinear Boundary Damping -- Formulation of the results -- Regularization -- Preliminary PDE inequalities -- Absorption of the lower-order terms -- Completion of the proof of the main theorem -- Nonlinear Plate Equations -- Modified von Karman equations -- Full von Karman system and dynamic system of elasticity -- Nonlinear plates with thermoelasticity -- Comments and Open Problems -- Uniform Stability of Structural Acoustic Models -- Orientation -- Internal Damping on the Wall -- Boundary Damping on the Wall -- Model -- Formulation of the results -- Preliminary multipliers estimates -- Microanalysis estimate for the traces of solutions of Euler-Bernoulli equations and wave equations -- Observability estimates for the structural acoustic problem -- Completion of the proof of Theorem 4.3.1 -- Thermal Damping -- Model -- Statement of main results -- Sharp trace regularity results -- Uniform stabilization: Proof of Theorem 4.4.2 -- Wave equation -- Uniform stability analysis for the coupled system -- Comments and Open Problems -- Structural Acoustic Control Problems: Semigroup and PDE Models -- Orientation -- Abstract Setting: Semigroup Formulation -- PDE Models Illustrating the Abstract Wall Equation (5.2.2) -- Plates and beams: Flat[Gamma subscript 0] -- "Undamped" boundary conditions: g [identical with] 0 in (5.3.10) -- Boundary feedback: Case g [not equal] 0 in (5.3.10) and related stability -- Shells: Curved-wall [Gamma subscript 0] -- Stability in Linear Structural Acoustic Models -- Internal damping on the wall -- Boundary damping on the wall -- Comments and Open Problems -- Feedback Noise Control in Structural Acoustic Models: Finite Horizon Problems -- Orientation -- Optimal Control Problem -- Formulation of the Results -- Hyperbolic-parabolic coupling -- Hyperbolic-hyperbolic coupling: General case -- Hyperbolic-hyperbolic coupling: Special case of the Kirchhoff plate with point control -- Abstract Optimal Control Problem: General Theory -- Formulation of the abstract control problem -- Characterization of the optimal control -- Additional properties under the hyperbolic regularity assumption -- DRE, feedback generator, and regularity of the gains B*P, B*r -- Riccati Equations Subject to the Singular Estimate for e[superscript At]B -- Formulation of the results -- Proof of Lemma 6.5.1 -- Proof of Theorem 6.5.1 -- Back to Structural Acoustic Problems: Proofs of Theorems 6.3.1 and 6.3.2 -- Verification of Assumption (6.4.1) -- Verification of Assumption 6.5.1 -- Comments and Open Problems -- Feedback Noise Control in Structural Acoustic Models: Infinite Horizon Problems -- Orientation -- Optimal Control Problem -- Formulation of the Results -- Hyperbolic-parabolic coupling -- Hyperbolic-hyperbolic coupling: Abstract results -- Hyperbolic-hyperbolic coupling: Kirchhoff plate with point control -- Abstract Optimal Control Problem: General Theory -- Formulation of the abstract control problem -- ARE subject to condition (7.4.15) -- ARE Subject to a Singular Estimate for e[superscript At]B -- Formulation of the results -- Proof of Theorem 7.5.1 -- Back to Structural Acoustic Problems: Proofs of Theorems 7.3.1 and 7.3.2 -- Comments and Open Problems -- Bibliography -- Index. 1. 1.1. 1.1.1. 1.1.2. 1.1.3. 1.2. 2. 2.1. 2.2. 2.3. 2.4. 2.4.1. 2.4.2. 2.5. 2.6. 2.7. 2.7.1. 2.7.2. 2.7.3. 2.8. 3. 3.1. 3.2. 3.3. 3.3.1. 3.3.2. 3.3.3. 3.3.4. 3.3.5. 3.4. 3.4.1. 3.4.2. 3.4.3. 3.5. 4. 4.1. 4.2. 4.3. 4.3.1. 4.3.2. 4.3.3. 4.3.4. 4.3.5. 4.3.6. 4.4. 4.4.1. 4.4.2. 4.4.3. 4.4.4. 4.4.5. 4.4.6. 4.5. 5. 5.1. 5.2. 5.3. 5.3.1. 5.3.2. 5.3.3. 5.3.4. 5.4. 5.4.1. 5.4.2. 5.5. 6. 6.1. 6.2. 6.3. 6.3.1. 6.3.2. 6.3.3. 6.4. 6.4.1. 6.4.2. 6.4.3. 6.4.4. 6.5. 6.5.1. 6.5.2. 6.5.3. 6.6. 6.6.1. 6.6.2. 6.7. 7. 7.1. 7.2. 7.3. 7.3.1. 7.3.2. 7.3.3. 7.4. 7.4.1. 7.4.2. 7.5. 7.5.1. 7.5.2. 7.6. 7.7.
0898714869 9780898714869
2001042994
Control theory
Differential equations, Hyperbolic
Differential equations, Parabolic
Coupled mode theory
QA402.3 / .L333 2002
629.8312
Mathematical control theory of coupled PDEs / Irena Lasiecka. - xii, 242 pages ; 25 cm. - CBMS-NSF regional conference series in applied mathematics ; 75 . - CBMS-NSF regional conference series in applied mathematics ; 75. .
Includes bibliographical references (pages 225-238) and index.
Preface -- Introduction -- Control Theory of Dynamical PDEs -- Finite- versus infinite-dimensional control theory -- Boundary/point control problems for single PDEs -- Boundary/point control problems for systems of coupled PDEs -- Goal of the Lectures -- Well-Posedness of Second-Order Nonlinear Equations with Boundary Damping -- Orientation -- Abstract Model -- Existence and Uniqueness: Statement of Main Results -- Nonlinear Plates: von Karman Equations -- Case [gamma] > 0 -- Case [gamma] = 0 -- Semilinear Wave Equation -- Nonlinear Structural Acoustic Model -- Full von Karman Systems -- Model -- Formulation of the results: Case [gamma] = 0 -- Formulation of the results: Case [gamma] > 0 -- Comments and Open Problems -- Uniform Stabilizability of Nonlinear Waves and Plates -- Orientation -- Abstract Stabilization Inequalities -- Semilinear Wave Equation with Nonlinear Boundary Damping -- Formulation of the results -- Regularization -- Preliminary PDE inequalities -- Absorption of the lower-order terms -- Completion of the proof of the main theorem -- Nonlinear Plate Equations -- Modified von Karman equations -- Full von Karman system and dynamic system of elasticity -- Nonlinear plates with thermoelasticity -- Comments and Open Problems -- Uniform Stability of Structural Acoustic Models -- Orientation -- Internal Damping on the Wall -- Boundary Damping on the Wall -- Model -- Formulation of the results -- Preliminary multipliers estimates -- Microanalysis estimate for the traces of solutions of Euler-Bernoulli equations and wave equations -- Observability estimates for the structural acoustic problem -- Completion of the proof of Theorem 4.3.1 -- Thermal Damping -- Model -- Statement of main results -- Sharp trace regularity results -- Uniform stabilization: Proof of Theorem 4.4.2 -- Wave equation -- Uniform stability analysis for the coupled system -- Comments and Open Problems -- Structural Acoustic Control Problems: Semigroup and PDE Models -- Orientation -- Abstract Setting: Semigroup Formulation -- PDE Models Illustrating the Abstract Wall Equation (5.2.2) -- Plates and beams: Flat[Gamma subscript 0] -- "Undamped" boundary conditions: g [identical with] 0 in (5.3.10) -- Boundary feedback: Case g [not equal] 0 in (5.3.10) and related stability -- Shells: Curved-wall [Gamma subscript 0] -- Stability in Linear Structural Acoustic Models -- Internal damping on the wall -- Boundary damping on the wall -- Comments and Open Problems -- Feedback Noise Control in Structural Acoustic Models: Finite Horizon Problems -- Orientation -- Optimal Control Problem -- Formulation of the Results -- Hyperbolic-parabolic coupling -- Hyperbolic-hyperbolic coupling: General case -- Hyperbolic-hyperbolic coupling: Special case of the Kirchhoff plate with point control -- Abstract Optimal Control Problem: General Theory -- Formulation of the abstract control problem -- Characterization of the optimal control -- Additional properties under the hyperbolic regularity assumption -- DRE, feedback generator, and regularity of the gains B*P, B*r -- Riccati Equations Subject to the Singular Estimate for e[superscript At]B -- Formulation of the results -- Proof of Lemma 6.5.1 -- Proof of Theorem 6.5.1 -- Back to Structural Acoustic Problems: Proofs of Theorems 6.3.1 and 6.3.2 -- Verification of Assumption (6.4.1) -- Verification of Assumption 6.5.1 -- Comments and Open Problems -- Feedback Noise Control in Structural Acoustic Models: Infinite Horizon Problems -- Orientation -- Optimal Control Problem -- Formulation of the Results -- Hyperbolic-parabolic coupling -- Hyperbolic-hyperbolic coupling: Abstract results -- Hyperbolic-hyperbolic coupling: Kirchhoff plate with point control -- Abstract Optimal Control Problem: General Theory -- Formulation of the abstract control problem -- ARE subject to condition (7.4.15) -- ARE Subject to a Singular Estimate for e[superscript At]B -- Formulation of the results -- Proof of Theorem 7.5.1 -- Back to Structural Acoustic Problems: Proofs of Theorems 7.3.1 and 7.3.2 -- Comments and Open Problems -- Bibliography -- Index. 1. 1.1. 1.1.1. 1.1.2. 1.1.3. 1.2. 2. 2.1. 2.2. 2.3. 2.4. 2.4.1. 2.4.2. 2.5. 2.6. 2.7. 2.7.1. 2.7.2. 2.7.3. 2.8. 3. 3.1. 3.2. 3.3. 3.3.1. 3.3.2. 3.3.3. 3.3.4. 3.3.5. 3.4. 3.4.1. 3.4.2. 3.4.3. 3.5. 4. 4.1. 4.2. 4.3. 4.3.1. 4.3.2. 4.3.3. 4.3.4. 4.3.5. 4.3.6. 4.4. 4.4.1. 4.4.2. 4.4.3. 4.4.4. 4.4.5. 4.4.6. 4.5. 5. 5.1. 5.2. 5.3. 5.3.1. 5.3.2. 5.3.3. 5.3.4. 5.4. 5.4.1. 5.4.2. 5.5. 6. 6.1. 6.2. 6.3. 6.3.1. 6.3.2. 6.3.3. 6.4. 6.4.1. 6.4.2. 6.4.3. 6.4.4. 6.5. 6.5.1. 6.5.2. 6.5.3. 6.6. 6.6.1. 6.6.2. 6.7. 7. 7.1. 7.2. 7.3. 7.3.1. 7.3.2. 7.3.3. 7.4. 7.4.1. 7.4.2. 7.5. 7.5.1. 7.5.2. 7.6. 7.7.
0898714869 9780898714869
2001042994
Control theory
Differential equations, Hyperbolic
Differential equations, Parabolic
Coupled mode theory
QA402.3 / .L333 2002
629.8312