Mathematical control theory of coupled PDEs:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
Society for Industrial and Applied Mathematics
2002
|
| Schriftenreihe: | CBMS-NSF regional conference series in applied mathematics
75 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 225-238) and index |
| Beschreibung: | XII, 242 S. |
| ISBN: | 0898714869 |
Internformat
MARC
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| 100 | 1 | |a Lasiecka, Irena |d 1948- |e Verfasser |0 (DE-588)111374383 |4 aut | |
| 245 | 1 | 0 | |a Mathematical control theory of coupled PDEs |c Irena Lasiecka |
| 264 | 1 | |a Philadelphia |b Society for Industrial and Applied Mathematics |c 2002 | |
| 300 | |a XII, 242 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a CBMS-NSF regional conference series in applied mathematics |v 75 | |
| 500 | |a Includes bibliographical references (p. 225-238) and index | ||
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Coupled mode theory | |
| 650 | 4 | |a Differential equations, Hyperbolic | |
| 650 | 4 | |a Differential equations, Parabolic | |
| 650 | 0 | 7 | |a Hyperbolisches Differentialgleichungssystem |0 (DE-588)4496581-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineares Differentialgleichungssystem |0 (DE-588)4229541-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kontrolltheorie |0 (DE-588)4032317-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Parabolisches Differentialgleichungssystem |0 (DE-588)4833677-4 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009878070 | ||
Datensatz im Suchindex
| _version_ | 1804129302541762560 |
|---|---|
| adam_text | Contents
Preface xi
1 Introduction 1
1.1 Control Theory of Dynamical PDEs 1
1.1.1 Finite versus infinite dimensional control theory 2
1.1.2 Boundary/point control problems for single PDEs 2
1.1.3 Boundary/point control problems for systems
of coupled PDEs 3
1.2 Goal of the Lectures 4
2 Well Posedness of Second Order Nonlinear Equations
with Boundary Damping 7
2.1 Orientation 7
2.2 Abstract Model 8
2.3 Existence and Uniqueness: Statement of Main
Results 9
2.4 Nonlinear Plates: von Karman Equations 13
2.4.1 Case 7 0 15
2.4.2 Case 7 = 0 19
2.5 Semilinear Wave Equation 21
2.6 Nonlinear Structural Acoustic Model 25
2.7 Full von Karman Systems 28
2.7.1 Model 28
2.7.2 Formulation of the results: Case 7 = 0 32
2.7.3 Formulation of the results: Case 7 0 34
2.8 Comments and Open Problems 37
3 Uniform Stabilizability of Nonlinear Waves and Plates 39
3.1 Orientation 39
3.2 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 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
viii CONTENTS
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 Nonlinear plates with thermoelasticity 77
3.5 Comments and Open Problems 82
4 Uniform Stability of Structural Acoustic Models 85
4.1 Orientation 85
4.2 Internal Damping on the Wall 86
4.3 Boundary Damping on the Wall 90
4.3.1 Model 90
4.3.2 Formulation of the results 92
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 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 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
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
5.1 Orientation 133
5.2 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 To 140
5.3.2 Undamped boundary conditions: g = 0 in (5.3.10) 143
5.3.3 Boundary feedback: Case g ^ 0 in (5.3.10)
and related stability 145
5.3.4 Shells: Curved wall To I51
5.4 Stability in Linear Structural Acoustic Models 155
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 Feedback Noise Control in Structural Acoustic Models:
Finite Horizon Problems 163
6.1 Orientation 163
6.2 Optimal Control Problem 165
6.3 Formulation of the Results 167
6.3.1 Hyperbolic parabolic coupling 167
6.3.2 Hyperbolic hyperbolic coupling: General case 168
CONTENTS ix
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
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 DRE, feedback generator, and regularity of the
gains B*P,B*r 179
6.5 Riccati Equations Subject to the Singular Estimate for eAtB .... 180
6.5.1 Formulation of the results 180
6.5.2 Proof of Lemma 6.5.1 181
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
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
7.1 Orientation 203
7.2 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 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
7.4.2 ARE subject to condition (7.4.15) 213
7.5 ARE Subject to a Singular Estimate for eAtB 214
7.5.1 Formulation of the results 214
7.5.2 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
7.7 Comments and Open Problems 222
Bibliography 225
Index 239
|
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| dewey-search | 629.8/312 |
| dewey-sort | 3629.8 3312 |
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| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
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| id | DE-604.BV014470209 |
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| indexdate | 2024-07-09T19:02:59Z |
| institution | BVB |
| isbn | 0898714869 |
| language | English |
| lccn | 2001042994 |
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| physical | XII, 242 S. |
| publishDate | 2002 |
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| series | CBMS-NSF regional conference series in applied mathematics |
| series2 | CBMS-NSF regional conference series in applied mathematics |
| spelling | Lasiecka, Irena 1948- Verfasser (DE-588)111374383 aut Mathematical control theory of coupled PDEs Irena Lasiecka Philadelphia Society for Industrial and Applied Mathematics 2002 XII, 242 S. txt rdacontent n rdamedia nc rdacarrier CBMS-NSF regional conference series in applied mathematics 75 Includes bibliographical references (p. 225-238) and index Control theory Coupled mode theory Differential equations, Hyperbolic Differential equations, Parabolic Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 gnd rswk-swf Nichtlineares Differentialgleichungssystem (DE-588)4229541-5 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Parabolisches Differentialgleichungssystem (DE-588)4833677-4 gnd rswk-swf Parabolisches Differentialgleichungssystem (DE-588)4833677-4 s Nichtlineares Differentialgleichungssystem (DE-588)4229541-5 s Kontrolltheorie (DE-588)4032317-1 s DE-604 Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 s CBMS-NSF regional conference series in applied mathematics 75 (DE-604)BV000016696 75 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009878070&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lasiecka, Irena 1948- Mathematical control theory of coupled PDEs CBMS-NSF regional conference series in applied mathematics Control theory Coupled mode theory Differential equations, Hyperbolic Differential equations, Parabolic Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 gnd Nichtlineares Differentialgleichungssystem (DE-588)4229541-5 gnd Kontrolltheorie (DE-588)4032317-1 gnd Parabolisches Differentialgleichungssystem (DE-588)4833677-4 gnd |
| subject_GND | (DE-588)4496581-3 (DE-588)4229541-5 (DE-588)4032317-1 (DE-588)4833677-4 |
| title | Mathematical control theory of coupled PDEs |
| title_auth | Mathematical control theory of coupled PDEs |
| title_exact_search | Mathematical control theory of coupled PDEs |
| title_full | Mathematical control theory of coupled PDEs Irena Lasiecka |
| title_fullStr | Mathematical control theory of coupled PDEs Irena Lasiecka |
| title_full_unstemmed | Mathematical control theory of coupled PDEs Irena Lasiecka |
| title_short | Mathematical control theory of coupled PDEs |
| title_sort | mathematical control theory of coupled pdes |
| topic | Control theory Coupled mode theory Differential equations, Hyperbolic Differential equations, Parabolic Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 gnd Nichtlineares Differentialgleichungssystem (DE-588)4229541-5 gnd Kontrolltheorie (DE-588)4032317-1 gnd Parabolisches Differentialgleichungssystem (DE-588)4833677-4 gnd |
| topic_facet | Control theory Coupled mode theory Differential equations, Hyperbolic Differential equations, Parabolic Hyperbolisches Differentialgleichungssystem Nichtlineares Differentialgleichungssystem Kontrolltheorie Parabolisches Differentialgleichungssystem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009878070&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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