Evolutionary integral equations and applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
[2012]
|
| Edition: | Repr. of the 1993 ed. |
| Series: | Modern Birkhäuser classics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXVI, 366 S. |
| ISBN: | 3034804989 9783034804981 |
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MARC
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Record in the Search Index
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| adam_text | Titel: Evolutionary integral equations and applications
Autor: Prüss, Jan
Jahr: 2012
Contents
Preface
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: /c-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 LP-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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| bvnumber | BV041118790 |
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| discipline | Mathematik |
| edition | Repr. of the 1993 ed. |
| format | Book |
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| id | DE-604.BV041118790 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:40:03Z |
| institution | BVB |
| isbn | 3034804989 9783034804981 |
| language | English |
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| physical | XXVI, 366 S. |
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| spelling | Prüss, Jan 1951-2018 Verfasser (DE-588)113443625 aut Evolutionary integral equations and applications Jan Prüss Repr. of the 1993 ed. Basel [u.a.] Birkhäuser [2012] XXVI, 366 S. txt rdacontent n rdamedia nc rdacarrier Modern Birkhäuser classics Volterra-Integralgleichung (DE-588)4234593-5 gnd rswk-swf Volterra-Integralgleichung (DE-588)4234593-5 s DE-604 Erscheint auch als Online-Ausgabe 978-3-0348-0499-8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026094834&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Prüss, Jan 1951-2018 Evolutionary integral equations and applications 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=026094834&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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