Shock waves and reaction diffusion equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1994
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften
258 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 632 S. graph. Darst. |
| ISBN: | 3540942599 0387942599 |
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| 100 | 1 | |a Smoller, Joel |d 1935- |e Verfasser |0 (DE-588)1024209652 |4 aut | |
| 245 | 1 | 0 | |a Shock waves and reaction diffusion equations |c Joel Smoller |
| 246 | 1 | 3 | |a Shock waves and reaction-diffusion equations |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1994 | |
| 300 | |a XXII, 632 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften |v 258 | |
| 650 | 7 | |a Chemische reacties |2 gtt | |
| 650 | 7 | |a Diffusievergelijkingen |2 gtt | |
| 650 | 4 | |a Ondes de choc | |
| 650 | 7 | |a Partiële differentiaalvergelijkingen |2 gtt | |
| 650 | 7 | |a Schokgolven |2 gtt | |
| 650 | 4 | |a Équations de réaction-diffusion | |
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Datensatz im Suchindex
| _version_ | 1804123960622710784 |
|---|---|
| adam_text | Contents
Acknowledgment vii
Preface to the Second Edition ix
Preface to the First Edition xi
List of Frequently Used Symbols xxi
PART I
Basic Linear Theory l
CHAPTER 1
Ill Posed Problems 3
§A. Some Examples 3
§B. Lewy s Example 7
CHAPTER 2
Characteristics and Initial Value Problems 13
CHAPTER 3
The One Dimensional Wave Equation 17
CHAPTER 4
Uniqueness and Energy Integrals 26
CHAPTER 5
Holmgren s Uniqueness Theorem 33
CHAPTER 6
An Initial Value Problem for a Hyperbolic Equation 39
CHAPTER 7
Distribution Theory 45
§A. A Cursory View 45
§B. Fundamental Solutions 52
§C. Appendix 61
xviii Contents
CHAPTER 8
Second Order Linear Elliptic Equations 64
§A. The Strong Maximum Principle 65
§B. A Priori Estimates 70
§C. Existence of Solutions 72
§D. Elliptic Regularity 76
CHAPTER 9
Second Order Linear Parabolic Equations 78
§A. The Heat Equation 78
§B. Strong Maximum Principles 83
PART II
Reaction Diffusion Equations 9i
CHAPTER 10
Comparison Theorems and Monotonicity Methods 93
§A. Comparison Theorems for Nonlinear Equations 93
§B. Upper and Lower Solutions 96
§C. Applications 99
CHAPTER 11
Linearization 106
§A. Spectral Theory for Self Adjoint Operators 106
§B. Linearized Stability 114
§C. Appendix: The Krein Rutman Theorem 122
CHAPTER 12
Topological Methods 126
§A. Degree Theory in R 126
§B. The Leray Schauder Degree 139
§C. An Introduction to Morse Theory 146
§D. A Rapid Course in Topology 156
CHAPTER 13
Bifurcation Theory 167
§A. The Implicit Function Theorem 168
§B. Stability of Bifurcating Solutions 176
§C. Some General Bifurcation Theorems 181
§D. Spontaneous Bifurcation; An Example 185
CHAPTER 14
Systems of Reaction Diffusion Equations 192
§A. Local Existence of Solutions 193
§B. Invariant Regions 198
§C. A Comparison Theorem 212
§D. Decay to Spatially Homogeneous Solutions 222
§E. A Lyapunov Function for Contracting Rectangles 227
§F. Applications to the Equations of Mathematical Ecology 230
Contents xix
PART III
The Theory of Shock Waves 237
CHAPTER 15
Discontinuous Solutions of Conservation Laws 239
§A. Discontinuous Solutions 241
§B. Weak Solutions of Conservation Laws 246
§C. Evolutionary Systems 254
§D. The Shock Inequalities 259
§E. Irreversibility 261
CHAPTER 16
The Single Conservation Law 265
§A. Existence of an Entropy Solution 266
§B. Uniqueness of the Entropy Solution 281
§C. Asymptotic Behavior of the Entropy Solution 291
§D. The Riemann Problem for a Scalar Conservation Law 301
CHAPTER 17
The Riemann Problem for Systems of Conservation Laws 306
§A. The/ System 306
§B. Shocks and Simple Waves 320
§C. Solution of the General Riemann Problem 334
CHAPTER 18
Applications to Gas Dynamics 337
§A. The Shock Inequalities 338
§B. The Riemann Problem in Gas Dynamics 346
§C. Interaction of Shock Waves 358
CHAPTER 19
The Glimm Difference Scheme 368
§A. The Interaction Estimate 369
§B. The Difference Approximation 376
§C. Convergence 385
CHAPTER 20
Riemann Invariants, Entropy, and Uniqueness 391
§A. Riemann Invariants 392
§B. A Concept of Entropy 397
§C. Solutions with Big Data 403
§D. Instability of Rarefaction Shocks 414
§E. Oleinik s Uniqueness Theorem 416
CHAPTER 21
Quasi Linear Parabolic Systems 426
§A. Gradient Systems 426
§B. Artificial Viscosity 431
§C. Isentropic Gas Dynamics 435
xx Contents
PART IV
The Conley Index 445
CHAPTER 22
The Conley Index 447
§A. An Impressionistic Overview 448
§B. Isolated Invariant Sets and Isolating Blocks 458
§C. The Homotopy Index 472
CHAPTER 23
Index Pairs and the Continuation Theorem 478
§A. Morse Decompositions and Index Pairs 479
§B. The Conley Index of an Isolated Invariant Set 486
§C. Continuation 494
§D. Some Further Remarks 502
CHAPTER 24
Travelling Waves 507
§A. The Structure of Weak Shock Waves 508
§B. The Structure of Magnetohydrodynamic Shock Waves 514
§C. Periodic Travelling Waves 521
§D. Stability of Steady State Solutions 530
§E. Instability of Equilibrium Solutions of the Neumann Problem 542
§F. Appendix: A Criterion for Nondegeneracy 549
CHAPTER 25
Recent Results 553
Section I. Reaction Diffusion Equations 553
§A. Stability of the Fitz Hugh Nagumo Travelling Pulse 553
§B. Symmetry Breaking 555
§C. A Bifurcation Theorem 559
§D. Equivariant Conley Index 563
§E. Application to Semilinear Elliptic Equations 566
Concluding Remarks 568
Section II. Theory of Shock Waves 569
§A. Compensated Compactness 569
§B. Stability of Shock Waves 576
§C. Miscellaneous Results 581
Section III. Conley Index Theory 583
§A. The Connection Index 583
§B. Conley s Connection Matrix 586
§C. Miscellaneous Results 590
Section IV. Stability of Travelling Waves—A Topological Approach 590
§A. Introduction 590
§B. The Search for 7p(L) 592
§C. Applications to Fast Slow Systems 598
References 603
Bibliography 607
Author Index 621
Subject Index 625
|
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| discipline | Physik Mathematik |
| edition | 2. ed. |
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| id | DE-604.BV009620329 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:38:04Z |
| institution | BVB |
| isbn | 3540942599 0387942599 |
| language | English |
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| physical | XXII, 632 S. graph. Darst. |
| publishDate | 1994 |
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| publisher | Springer |
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| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Smoller, Joel 1935- Verfasser (DE-588)1024209652 aut Shock waves and reaction diffusion equations Joel Smoller Shock waves and reaction-diffusion equations 2. ed. New York [u.a.] Springer 1994 XXII, 632 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 258 Chemische reacties gtt Diffusievergelijkingen gtt Ondes de choc Partiële differentiaalvergelijkingen gtt Schokgolven gtt Équations de réaction-diffusion Reaction-diffusion equations Shock waves Diffusionsgleichung (DE-588)4149816-1 gnd rswk-swf Diffusion (DE-588)4012277-3 gnd rswk-swf Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Druckwelle (DE-588)4150776-9 gnd rswk-swf Stoßwelle (DE-588)4057760-0 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Stoßwelle (DE-588)4057760-0 s Diffusionsgleichung (DE-588)4149816-1 s DE-604 Reaktions-Diffusionsgleichung (DE-588)4323967-5 s Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Partielle Differentialgleichung (DE-588)4044779-0 s Druckwelle (DE-588)4150776-9 s Diffusion (DE-588)4012277-3 s Grundlehren der mathematischen Wissenschaften 258 (DE-604)BV000000395 258 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006358304&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Smoller, Joel 1935- Shock waves and reaction diffusion equations Grundlehren der mathematischen Wissenschaften Chemische reacties gtt Diffusievergelijkingen gtt Ondes de choc Partiële differentiaalvergelijkingen gtt Schokgolven gtt Équations de réaction-diffusion Reaction-diffusion equations Shock waves Diffusionsgleichung (DE-588)4149816-1 gnd Diffusion (DE-588)4012277-3 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Druckwelle (DE-588)4150776-9 gnd Stoßwelle (DE-588)4057760-0 gnd |
| subject_GND | (DE-588)4149816-1 (DE-588)4012277-3 (DE-588)4323967-5 (DE-588)4044779-0 (DE-588)4128900-6 (DE-588)4150776-9 (DE-588)4057760-0 (DE-588)1071861417 |
| title | Shock waves and reaction diffusion equations |
| title_alt | Shock waves and reaction-diffusion equations |
| title_auth | Shock waves and reaction diffusion equations |
| title_exact_search | Shock waves and reaction diffusion equations |
| title_full | Shock waves and reaction diffusion equations Joel Smoller |
| title_fullStr | Shock waves and reaction diffusion equations Joel Smoller |
| title_full_unstemmed | Shock waves and reaction diffusion equations Joel Smoller |
| title_short | Shock waves and reaction diffusion equations |
| title_sort | shock waves and reaction diffusion equations |
| topic | Chemische reacties gtt Diffusievergelijkingen gtt Ondes de choc Partiële differentiaalvergelijkingen gtt Schokgolven gtt Équations de réaction-diffusion Reaction-diffusion equations Shock waves Diffusionsgleichung (DE-588)4149816-1 gnd Diffusion (DE-588)4012277-3 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Druckwelle (DE-588)4150776-9 gnd Stoßwelle (DE-588)4057760-0 gnd |
| topic_facet | Chemische reacties Diffusievergelijkingen Ondes de choc Partiële differentiaalvergelijkingen Schokgolven Équations de réaction-diffusion Reaction-diffusion equations Shock waves Diffusionsgleichung Diffusion Reaktions-Diffusionsgleichung Partielle Differentialgleichung Nichtlineare partielle Differentialgleichung Druckwelle Stoßwelle Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006358304&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT smollerjoel shockwavesandreactiondiffusionequations |