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The Resource Mathematical control theory of coupled PDEs, Irena Lasiecka

Mathematical control theory of coupled PDEs, Irena Lasiecka

Label
Mathematical control theory of coupled PDEs
Title
Mathematical control theory of coupled PDEs
Statement of responsibility
Irena Lasiecka
Creator
Subject
Language
eng
Member of
Cataloging source
DLC
http://library.link/vocab/creatorDate
1948-
http://library.link/vocab/creatorName
Lasiecka, I.
Dewey number
629.8/312
Illustrations
illustrations
Index
index present
LC call number
QA402.3
LC item number
.L333 2002
Literary form
non fiction
Nature of contents
bibliography
Series statement
CBMS-NSF regional conference series in applied mathematics
Series volume
75
http://library.link/vocab/subjectName
  • Control theory
  • Differential equations, Hyperbolic
  • Differential equations, Parabolic
  • Coupled mode theory
Label
Mathematical control theory of coupled PDEs, Irena Lasiecka
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 225-238) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 2
  • 86
  • 4.3
  • Boundary Damping on the Wall
  • 90
  • 4.3.1
  • Model
  • 90
  • 4.3.2
  • Formulation of the results
  • 92
  • 1.1.3
  • 4.3.3
  • Preliminary multipliers estimates
  • 97
  • 4.3.4
  • Microanalysis estimate for the traces of solutions of Euler-Bernoulli equations and wave equations
  • 101
  • 4.3.5
  • Observability estimates for the structural acoustic problem
  • 104
  • 4.3.6
  • Boundary/point control problems for systems of coupled PDEs
  • Completion of the proof of Theorem 4.3.1
  • 109
  • 4.4
  • Thermal Damping
  • 110
  • 4.4.1
  • Model
  • 110
  • 4.4.2
  • Statement of main results
  • 3
  • 112
  • 4.4.3
  • Sharp trace regularity results
  • 115
  • 4.4.4
  • Uniform stabilization: Proof of Theorem 4.4.2
  • 117
  • 4.4.5
  • Wave equation
  • 124
  • 1.2
  • 4.4.6
  • Uniform stability analysis for the coupled system
  • 126
  • 4.5
  • Comments and Open Problems
  • 130
  • 5
  • Structural Acoustic Control Problems: Semigroup and PDE Models
  • 133
  • 5.2
  • Goal of the Lectures
  • Abstract Setting: Semigroup Formulation
  • 135
  • 5.3
  • PDE Models Illustrating the Abstract Wall Equation (5.2.2)
  • 140
  • 5.3.1
  • Plates and beams: Flat[Gamma subscript 0]
  • 140
  • 5.3.2
  • "Undamped" boundary conditions: g [identical with] 0 in (5.3.10)
  • 4
  • 143
  • 5.3.3
  • Boundary feedback: Case g [not equal] 0 in (5.3.10) and related stability
  • 145
  • 5.3.4
  • Shells: Curved-wall [Gamma subscript 0]
  • 151
  • 5.4
  • Stability in Linear Structural Acoustic Models
  • 155
  • 2
  • 5.4.1
  • Internal damping on the wall
  • 156
  • 5.4.2
  • Boundary damping on the wall
  • 158
  • 5.5
  • Comments and Open Problems
  • 160
  • 6
  • Well-Posedness of Second-Order Nonlinear Equations with Boundary Damping
  • Feedback Noise Control in Structural Acoustic Models: Finite Horizon Problems
  • 163
  • 6.2
  • Optimal Control Problem
  • 165
  • 6.3
  • Formulation of the Results
  • 167
  • 6.3.1
  • Hyperbolic-parabolic coupling
  • 7
  • 167
  • 6.3.2
  • Hyperbolic-hyperbolic coupling: General case
  • 168
  • 6.3.3
  • Hyperbolic-hyperbolic coupling: Special case of the Kirchhoff plate with point control
  • 169
  • 6.4
  • Abstract Optimal Control Problem: General Theory
  • 174
  • 1.1
  • 2.2
  • 6.4.1
  • Formulation of the abstract control problem
  • 174
  • 6.4.2
  • Characterization of the optimal control
  • 175
  • 6.4.3
  • Additional properties under the hyperbolic regularity assumption
  • 177
  • 6.4.4
  • Abstract Model
  • DRE, feedback generator, and regularity of the gains B*P, B*r
  • 179
  • 6.5
  • Riccati Equations Subject to the Singular Estimate for e[superscript At]B
  • 180
  • 6.5.1
  • Formulation of the results
  • 180
  • 6.5.2
  • Proof of Lemma 6.5.1
  • 8
  • 181
  • 6.5.3
  • Proof of Theorem 6.5.1
  • 187
  • 6.6
  • Back to Structural Acoustic Problems: Proofs of Theorems 6.3.1 and 6.3.2
  • 190
  • 6.6.1
  • Verification of Assumption (6.4.1)
  • 192
  • 2.3
  • 6.6.2
  • Verification of Assumption 6.5.1
  • 193
  • 6.7
  • Comments and Open Problems
  • 201
  • 7
  • Feedback Noise Control in Structural Acoustic Models: Infinite Horizon Problems
  • 203
  • 7.2
  • Existence and Uniqueness: Statement of Main Results
  • Optimal Control Problem
  • 205
  • 7.3
  • Formulation of the Results
  • 206
  • 7.3.1
  • Hyperbolic-parabolic coupling
  • 206
  • 7.3.2
  • Hyperbolic-hyperbolic coupling: Abstract results
  • 9
  • 208
  • 7.3.3
  • Hyperbolic-hyperbolic coupling: Kirchhoff plate with point control
  • 209
  • 7.4
  • Abstract Optimal Control Problem: General Theory
  • 212
  • 7.4.1
  • Formulation of the abstract control problem
  • 212
  • 2.4
  • 7.4.2
  • ARE subject to condition (7.4.15)
  • 213
  • 7.5
  • ARE Subject to a Singular Estimate for e[superscript At]B
  • 214
  • 7.5.1
  • Formulation of the results
  • 214
  • 7.5.2
  • Nonlinear Plates: von Karman Equations
  • Proof of Theorem 7.5.1
  • 215
  • 7.6
  • Back to Structural Acoustic Problems: Proofs of Theorems 7.3.1 and 7.3.2
  • 222
  • 13
  • 2.4.1
  • Control Theory of Dynamical PDEs
  • Case [gamma] > 0
  • 15
  • 2.4.2
  • Case [gamma] = 0
  • 19
  • 2.5
  • Semilinear Wave Equation
  • 21
  • 2.6
  • Nonlinear Structural Acoustic Model
  • 1
  • 25
  • 2.7
  • Full von Karman Systems
  • 28
  • 2.7.1
  • Model
  • 28
  • 2.7.2
  • Formulation of the results: Case [gamma] = 0
  • 32
  • 1.1.1
  • 2.7.3
  • Formulation of the results: Case [gamma] > 0
  • 34
  • 2.8
  • Comments and Open Problems
  • 37
  • 3
  • Uniform Stabilizability of Nonlinear Waves and Plates
  • 39
  • 3.2
  • Finite- versus infinite-dimensional control theory
  • Abstract Stabilization Inequalities
  • 41
  • 3.3
  • Semilinear Wave Equation with Nonlinear Boundary Damping
  • 45
  • 3.3.1
  • Formulation of the results
  • 47
  • 3.3.2
  • Regularization
  • 2
  • 51
  • 3.3.3
  • Preliminary PDE inequalities
  • 56
  • 3.3.4
  • Absorption of the lower-order terms
  • 61
  • 3.3.5
  • Completion of the proof of the main theorem
  • 66
  • 1.1.2
  • 3.4
  • Nonlinear Plate Equations
  • 67
  • 3.4.1
  • Modified von Karman equations
  • 67
  • 3.4.2
  • Full von Karman system and dynamic system of elasticity
  • 72
  • 3.4.3
  • Boundary/point control problems for single PDEs
  • Nonlinear plates with thermoelasticity
  • 77
  • 3.5
  • Comments and Open Problems
  • 82
  • 4
  • Uniform Stability of Structural Acoustic Models
  • 85
  • 4.2
  • Internal Damping on the Wall
Control code
47254274
Dimensions
25 cm
Extent
xii, 242 pages
Isbn
9780898714869
Isbn Type
(pbk.)
Lccn
2001042994
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
Label
Mathematical control theory of coupled PDEs, Irena Lasiecka
Publication
Bibliography note
Includes bibliographical references (pages 225-238) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 2
  • 86
  • 4.3
  • Boundary Damping on the Wall
  • 90
  • 4.3.1
  • Model
  • 90
  • 4.3.2
  • Formulation of the results
  • 92
  • 1.1.3
  • 4.3.3
  • Preliminary multipliers estimates
  • 97
  • 4.3.4
  • Microanalysis estimate for the traces of solutions of Euler-Bernoulli equations and wave equations
  • 101
  • 4.3.5
  • Observability estimates for the structural acoustic problem
  • 104
  • 4.3.6
  • Boundary/point control problems for systems of coupled PDEs
  • Completion of the proof of Theorem 4.3.1
  • 109
  • 4.4
  • Thermal Damping
  • 110
  • 4.4.1
  • Model
  • 110
  • 4.4.2
  • Statement of main results
  • 3
  • 112
  • 4.4.3
  • Sharp trace regularity results
  • 115
  • 4.4.4
  • Uniform stabilization: Proof of Theorem 4.4.2
  • 117
  • 4.4.5
  • Wave equation
  • 124
  • 1.2
  • 4.4.6
  • Uniform stability analysis for the coupled system
  • 126
  • 4.5
  • Comments and Open Problems
  • 130
  • 5
  • Structural Acoustic Control Problems: Semigroup and PDE Models
  • 133
  • 5.2
  • Goal of the Lectures
  • Abstract Setting: Semigroup Formulation
  • 135
  • 5.3
  • PDE Models Illustrating the Abstract Wall Equation (5.2.2)
  • 140
  • 5.3.1
  • Plates and beams: Flat[Gamma subscript 0]
  • 140
  • 5.3.2
  • "Undamped" boundary conditions: g [identical with] 0 in (5.3.10)
  • 4
  • 143
  • 5.3.3
  • Boundary feedback: Case g [not equal] 0 in (5.3.10) and related stability
  • 145
  • 5.3.4
  • Shells: Curved-wall [Gamma subscript 0]
  • 151
  • 5.4
  • Stability in Linear Structural Acoustic Models
  • 155
  • 2
  • 5.4.1
  • Internal damping on the wall
  • 156
  • 5.4.2
  • Boundary damping on the wall
  • 158
  • 5.5
  • Comments and Open Problems
  • 160
  • 6
  • Well-Posedness of Second-Order Nonlinear Equations with Boundary Damping
  • Feedback Noise Control in Structural Acoustic Models: Finite Horizon Problems
  • 163
  • 6.2
  • Optimal Control Problem
  • 165
  • 6.3
  • Formulation of the Results
  • 167
  • 6.3.1
  • Hyperbolic-parabolic coupling
  • 7
  • 167
  • 6.3.2
  • Hyperbolic-hyperbolic coupling: General case
  • 168
  • 6.3.3
  • Hyperbolic-hyperbolic coupling: Special case of the Kirchhoff plate with point control
  • 169
  • 6.4
  • Abstract Optimal Control Problem: General Theory
  • 174
  • 1.1
  • 2.2
  • 6.4.1
  • Formulation of the abstract control problem
  • 174
  • 6.4.2
  • Characterization of the optimal control
  • 175
  • 6.4.3
  • Additional properties under the hyperbolic regularity assumption
  • 177
  • 6.4.4
  • Abstract Model
  • DRE, feedback generator, and regularity of the gains B*P, B*r
  • 179
  • 6.5
  • Riccati Equations Subject to the Singular Estimate for e[superscript At]B
  • 180
  • 6.5.1
  • Formulation of the results
  • 180
  • 6.5.2
  • Proof of Lemma 6.5.1
  • 8
  • 181
  • 6.5.3
  • Proof of Theorem 6.5.1
  • 187
  • 6.6
  • Back to Structural Acoustic Problems: Proofs of Theorems 6.3.1 and 6.3.2
  • 190
  • 6.6.1
  • Verification of Assumption (6.4.1)
  • 192
  • 2.3
  • 6.6.2
  • Verification of Assumption 6.5.1
  • 193
  • 6.7
  • Comments and Open Problems
  • 201
  • 7
  • Feedback Noise Control in Structural Acoustic Models: Infinite Horizon Problems
  • 203
  • 7.2
  • Existence and Uniqueness: Statement of Main Results
  • Optimal Control Problem
  • 205
  • 7.3
  • Formulation of the Results
  • 206
  • 7.3.1
  • Hyperbolic-parabolic coupling
  • 206
  • 7.3.2
  • Hyperbolic-hyperbolic coupling: Abstract results
  • 9
  • 208
  • 7.3.3
  • Hyperbolic-hyperbolic coupling: Kirchhoff plate with point control
  • 209
  • 7.4
  • Abstract Optimal Control Problem: General Theory
  • 212
  • 7.4.1
  • Formulation of the abstract control problem
  • 212
  • 2.4
  • 7.4.2
  • ARE subject to condition (7.4.15)
  • 213
  • 7.5
  • ARE Subject to a Singular Estimate for e[superscript At]B
  • 214
  • 7.5.1
  • Formulation of the results
  • 214
  • 7.5.2
  • Nonlinear Plates: von Karman Equations
  • Proof of Theorem 7.5.1
  • 215
  • 7.6
  • Back to Structural Acoustic Problems: Proofs of Theorems 7.3.1 and 7.3.2
  • 222
  • 13
  • 2.4.1
  • Control Theory of Dynamical PDEs
  • Case [gamma] > 0
  • 15
  • 2.4.2
  • Case [gamma] = 0
  • 19
  • 2.5
  • Semilinear Wave Equation
  • 21
  • 2.6
  • Nonlinear Structural Acoustic Model
  • 1
  • 25
  • 2.7
  • Full von Karman Systems
  • 28
  • 2.7.1
  • Model
  • 28
  • 2.7.2
  • Formulation of the results: Case [gamma] = 0
  • 32
  • 1.1.1
  • 2.7.3
  • Formulation of the results: Case [gamma] > 0
  • 34
  • 2.8
  • Comments and Open Problems
  • 37
  • 3
  • Uniform Stabilizability of Nonlinear Waves and Plates
  • 39
  • 3.2
  • Finite- versus infinite-dimensional control theory
  • Abstract Stabilization Inequalities
  • 41
  • 3.3
  • Semilinear Wave Equation with Nonlinear Boundary Damping
  • 45
  • 3.3.1
  • Formulation of the results
  • 47
  • 3.3.2
  • Regularization
  • 2
  • 51
  • 3.3.3
  • Preliminary PDE inequalities
  • 56
  • 3.3.4
  • Absorption of the lower-order terms
  • 61
  • 3.3.5
  • Completion of the proof of the main theorem
  • 66
  • 1.1.2
  • 3.4
  • Nonlinear Plate Equations
  • 67
  • 3.4.1
  • Modified von Karman equations
  • 67
  • 3.4.2
  • Full von Karman system and dynamic system of elasticity
  • 72
  • 3.4.3
  • Boundary/point control problems for single PDEs
  • Nonlinear plates with thermoelasticity
  • 77
  • 3.5
  • Comments and Open Problems
  • 82
  • 4
  • Uniform Stability of Structural Acoustic Models
  • 85
  • 4.2
  • Internal Damping on the Wall
Control code
47254274
Dimensions
25 cm
Extent
xii, 242 pages
Isbn
9780898714869
Isbn Type
(pbk.)
Lccn
2001042994
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations

Library Locations

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      38.710138 -90.311107
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