Evolutionary integral equations and applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
1993
|
| Series: | Monographs in mathematics
87 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXVI, 366 S. |
| ISBN: | 3764328762 0817628762 |
Staff View
MARC
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| 245 | 1 | 0 | |a Evolutionary integral equations and applications |c Jan Prüss |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ix
Introduction xi
1 Evolutionary Integral Equations xi
2 Model Problems xii
3 Preliminary Discussions xv
4 Equations of Scalar Type xvii
5 Nonscalar Problems xx
6 Equations on the Line xxiii
0 Preliminaries 1
0.1 Some Notation 1
0.2 Laplace Transform 4
0.3 Volterra Equations with Bounded Kernels 12
0.4 Convolution Equations with Bounded Kernels on the Line . 15
0.5 The Spectrum of Functions of Subexponential Growth ... 19
0.6 The Spectrum of Functions Growing Polynomially 22
I Equations of Scalar Type
1 Resolvents 30
1.1 Well posedness and Resolvents 30
1.2 Inhomogeneous Equations 33
1.3 Necessary Conditions for Well posedness 36
1.4 Perturbed Equations 39
1.5 The Generation Theorem 42
1.6 Integral Resolvents 45
1.7 Comments 47
2 Analytic Resolvents 49
2.1 Definition and First Properties 49
2.2 Generation of Analytic Resolvents 52
2.3 Examples 55
2.4 Spatial Regularity 56
vi Contents
2.5 Perturbed Equations 60
2.6 Maximal Regularity 62
2.7 Comments 64
3 Parabolic Equations 68
3.1 Parabolicity 68
3.2 Regular Kernels 69
3.3 Resolvents for Parabolic Equations 73
3.4 Perturbations 76
3.5 Maximal Regularity 77
3.6 A Representation Formula 79
3.7 Comments 81
Appendix: fc monotone Kernels 83
4 Subordination 90
4.1 Bernstein Functions 90
4.2 Completely Positive Kernels 94
4.3 The Subordination Principle 99
4.4 Equations with Completely Positive Kernels 103
4.5 Propagation Functions 106
4.6 Structure of Subordinated Resolvents 110
4.7 Comments 115
Appendix: Some Common Bernstein Functions 119
5 Linear Viscoelasticity 122
5.1 Balance of Momentum and Constitutive Laws 122
5.2 Material Functions 128
5.3 Energy Balance and Thermoviscoelasticity 132
5.4 Some One dimensional Problems 135
5.5 Heat Conduction in Materials with Memory 139
5.6 Synchronous and Incompressible Materials 141
5.7 A Simple Control Problem 146
5.8 Comments 148
II Nonscalar Equations
6 Hyperbolic Equations of Nonscalar Type 152
6.1 Resolvents of Nonscalar Equations 152
6.2 Well posedness and Variation of Parameters Formulae . . . 155
6.3 Hyperbolic Perturbation Results 159
6.4 The Generation Theorem 162
6.5 Convergence of Resolvents 167
6.6 Kernels of Positive Type in Hilbert spaces 170
6.7 Hyperbolic Problems of Variational Type 175
6.8 Comments 182
Contents vii
7 Nonscalar Parabolic Equations 185
7.1 Analytic Resolvents 185
7.2 Parabolic Equations 188
7.3 Parabolic Problems of Variational Type 190
7.4 Maximal Regularity of Perturbed Parabolic Problems . . . 193
7.5 Resolvents for Perturbed Parabolic Problems 197
7.6 Uniform Bounds for the Resolvent 201
7.7 Comments 211
8 Parabolic Problems in LP Spaces 212
8.1 Operators with Bounded Imaginary Powers 212
8.2 Vector Valued Multiplier Theorems 215
8.3 Sums of Commuting Linear Operators 217
8.4 Volterra Operators in Lp 221
8.5 Maximal Regularity in Lp 227
8.6 Strong /^ Stability on the Halfline 229
8.7 Comments 232
9 Viscoelasticity and Electrodynamics with Memory 236
9.1 Viscoelastic Beams 236
9.2 Viscoelastic Plates 240
9.3 Thermoviscoelasticity: Strong Approach 242
9.4 Thermoviscoelasticity: Variational Approach 246
9.5 Electrodynamics with Memory 248
9.6 A Transmission Problem for Media with Memory 251
9.7 Comments 253
III Equations on the Line
10 Integrability of Resolvents 256
10.1 Stability on the Halfline 256
10.2 Parabolic Equations of Scalar Type 260
10.3 Subordinated Resolvents 266
10.4 Strong Integrability in Hilbert Spaces 272
10.5 Nonscalar Parabolic Problems 277
10.6 Comments 281
11 Limiting Equations 284
11.1 Homogeneous Spaces 284
11.2 Admissibility 287
11.3 A Kernels for Compact A 289
11.4 Almost Periodic Solutions 293
11.5 Nonresonant Problems 296
11.6 Asymptotic Equivalence 299
11.7 Comments 303
viii Contents
12 Admissibility of Function Spaces 306
12.1 Perturbations: Hyperbolic Case 306
12.2 Subordinated Equations 308
12.3 Admissibility in Hilbert Spaces 310
12.4 A kernels for Parabolic Problems 315
12.5 Maximal Regularity on the Line 318
12.6 Perturbations: Parabolic Case 320
12.7 Comments 322
13 Further Applications and Complements 323
13.1 Viscoelastic Timoshenko Beams 323
13.2 Heat Conduction in Materials with Memory 326
13.3 Electrodynamics with Memory 329
13.4 Ergodic Theory 333
13.5 Semilinear Equations 335
13.6 Semigroup Approaches 338
13.7 Nonlinear Equations with Accretive Operators 342
Bibliography 347
Index 363
|
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| discipline | Mathematik |
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| id | DE-604.BV007745897 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:08:48Z |
| institution | BVB |
| isbn | 3764328762 0817628762 |
| language | English |
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| physical | XXVI, 366 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Monographs in mathematics |
| series2 | Monographs in mathematics |
| spelling | Prüss, Jan 1951-2018 Verfasser (DE-588)113443625 aut Evolutionary integral equations and applications Jan Prüss Basel [u.a.] Birkhäuser 1993 XXVI, 366 S. txt rdacontent n rdamedia nc rdacarrier Monographs in mathematics 87 Volterra-Integralgleichung (DE-588)4234593-5 gnd rswk-swf Volterra-Integralgleichung (DE-588)4234593-5 s DE-604 Monographs in mathematics 87 (DE-604)BV000008284 87 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005093364&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Prüss, Jan 1951-2018 Evolutionary integral equations and applications Monographs in mathematics Volterra-Integralgleichung (DE-588)4234593-5 gnd |
| subject_GND | (DE-588)4234593-5 |
| title | Evolutionary integral equations and applications |
| title_auth | Evolutionary integral equations and applications |
| title_exact_search | Evolutionary integral equations and applications |
| title_full | Evolutionary integral equations and applications Jan Prüss |
| title_fullStr | Evolutionary integral equations and applications Jan Prüss |
| title_full_unstemmed | Evolutionary integral equations and applications Jan Prüss |
| title_short | Evolutionary integral equations and applications |
| title_sort | evolutionary integral equations and applications |
| topic | Volterra-Integralgleichung (DE-588)4234593-5 gnd |
| topic_facet | Volterra-Integralgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005093364&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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