Spatial patterns: higher order models in physics and mechanics
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2001
|
| Schriftenreihe: | Progress in nonlinear differential equations and their applications
45 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 321 - 335 |
| Beschreibung: | XV, 341 S. Ill., graph. Darst. |
| ISBN: | 3764341106 0817641106 |
Internformat
MARC
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| 245 | 1 | 0 | |a Spatial patterns |b higher order models in physics and mechanics |c L. A. Peletier ; W. C. Troy |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2001 | |
| 300 | |a XV, 341 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in nonlinear differential equations and their applications |v 45 | |
| 500 | |a Literaturverz. S. 321 - 335 | ||
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| 650 | 7 | |a Partiële differentiaalvergelijkingen |2 gtt | |
| 650 | 4 | |a Équations aux dérivées partielles - Solutions numériques | |
| 650 | 4 | |a Équations différentielles - Solutions numériques | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Differential equations |x Numerical solutions | |
| 650 | 4 | |a Differential equations, Partial |x Numerical solutions | |
| 650 | 4 | |a Pattern formation (Physical sciences) |x Mathematical models | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface ix
Outline xiii
1 Introduction 1
1.1 Model equations 2
1.2 The Fisher Kolmogorov equation 10
1.3 An overview 13
1.4 Methods 27
1.5 About the presentation 36
1.6 Bibliographical notes 39
1 The Symmetric Bistable Equation 41
2 Real Eigenvalues 43
2.1 Periodic solutions 44
2.2 Kinks (1) 50
2.3 Kinks (2) 53
2.4 Uniqueness 57
2.5 Qualitative properties 64
3 Estimates 69
3.1 Critical points 70
3.2 Bounds 83
3.3 A limit theorem 95
vi Contents
4 Periodic Solutions 101
4.1 Odd periodic solutions 101
4.2 Asymptotics 116
4.3 Even periodic solutions up to q = J 122
4.4 Linearisation at u = 1 133
4.5 Even periodic solutions beyond q = V8 139
4.6 Periodic solutions with nonzero energy (E ^ 0) 156
5 Kinks and Pulses 173
5.1 Kinks 173
5.2 Pulses 190
6 Chaotic Solutions 197
6.1 Chaotic solutions 198
6.2 The Induction Lemma 201
6.3 The construction 204
6.4 The Falkner Skan equation 210
6.5 The Kuramoto Sivashinsky equation 213
7 Variational Problems 219
7.1 The problem 219
7.2 Bounds 223
7.3 Symmetry properties 227
7.4 Existence of kinks 231
7.5 Bibliographical notes 235
II Related Equations 237
8 The Asymmetric Double Well Potential 239
8.1 Preliminary observations 240
8.2 Real eigenvalues 243
8.3 Complex eigenvalues 246
8.4 Periodic solutions with nonzero energy (E ^ 0) 259
8.5 Periodic solutions in the (a, Af) plane 266
8.6 Discussion 273
9 The Swift Hohenberg Equation 275
9.1 Preliminaries 276
9.2 Odd single bump periodic solutions 277
9.3 Multibump periodic solutions 284
9.4 The region where k 1 289
9.5 Generalisations 294
10 Waves in Nonlinearly Supported Beams 307
10.1 The beam equation 307
Contents vii
10.2 Single bump periodic solutions 310
10.3 Multibump periodic solutions 314
References 321
Index 337
|
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| indexdate | 2024-07-09T18:54:09Z |
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| language | English |
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| physical | XV, 341 S. Ill., graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in nonlinear differential equations and their applications |
| series2 | Progress in nonlinear differential equations and their applications |
| spelling | Peletier, Lambert A. Verfasser aut Spatial patterns higher order models in physics and mechanics L. A. Peletier ; W. C. Troy Boston [u.a.] Birkhäuser 2001 XV, 341 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in nonlinear differential equations and their applications 45 Literaturverz. S. 321 - 335 Formation des structures (Sciences physiques) - Modèles mathématiques Gewone differentiaalvergelijkingen gtt Korteweg-De Vries vergelijkingen gtt Modellen (vorm) gtt Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles - Solutions numériques Équations différentielles - Solutions numériques Mathematisches Modell Differential equations Numerical solutions Differential equations, Partial Numerical solutions Pattern formation (Physical sciences) Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Strukturbildung (DE-588)4541700-3 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Ordnung n (DE-588)4322729-6 gnd rswk-swf Physikalisches System (DE-588)4174610-7 gnd rswk-swf Physikalisches System (DE-588)4174610-7 s Strukturbildung (DE-588)4541700-3 s Mathematisches Modell (DE-588)4114528-8 s Nichtlineare Differentialgleichung (DE-588)4205536-2 s Ordnung n (DE-588)4322729-6 s DE-604 Troy, William C. Verfasser aut Progress in nonlinear differential equations and their applications 45 (DE-604)BV007934389 45 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009514331&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Peletier, Lambert A. Troy, William C. Spatial patterns higher order models in physics and mechanics Progress in nonlinear differential equations and their applications Formation des structures (Sciences physiques) - Modèles mathématiques Gewone differentiaalvergelijkingen gtt Korteweg-De Vries vergelijkingen gtt Modellen (vorm) gtt Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles - Solutions numériques Équations différentielles - Solutions numériques Mathematisches Modell Differential equations Numerical solutions Differential equations, Partial Numerical solutions Pattern formation (Physical sciences) Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Strukturbildung (DE-588)4541700-3 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Ordnung n (DE-588)4322729-6 gnd Physikalisches System (DE-588)4174610-7 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4541700-3 (DE-588)4205536-2 (DE-588)4322729-6 (DE-588)4174610-7 |
| title | Spatial patterns higher order models in physics and mechanics |
| title_auth | Spatial patterns higher order models in physics and mechanics |
| title_exact_search | Spatial patterns higher order models in physics and mechanics |
| title_full | Spatial patterns higher order models in physics and mechanics L. A. Peletier ; W. C. Troy |
| title_fullStr | Spatial patterns higher order models in physics and mechanics L. A. Peletier ; W. C. Troy |
| title_full_unstemmed | Spatial patterns higher order models in physics and mechanics L. A. Peletier ; W. C. Troy |
| title_short | Spatial patterns |
| title_sort | spatial patterns higher order models in physics and mechanics |
| title_sub | higher order models in physics and mechanics |
| topic | Formation des structures (Sciences physiques) - Modèles mathématiques Gewone differentiaalvergelijkingen gtt Korteweg-De Vries vergelijkingen gtt Modellen (vorm) gtt Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles - Solutions numériques Équations différentielles - Solutions numériques Mathematisches Modell Differential equations Numerical solutions Differential equations, Partial Numerical solutions Pattern formation (Physical sciences) Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Strukturbildung (DE-588)4541700-3 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Ordnung n (DE-588)4322729-6 gnd Physikalisches System (DE-588)4174610-7 gnd |
| topic_facet | Formation des structures (Sciences physiques) - Modèles mathématiques Gewone differentiaalvergelijkingen Korteweg-De Vries vergelijkingen Modellen (vorm) Partiële differentiaalvergelijkingen Équations aux dérivées partielles - Solutions numériques Équations différentielles - Solutions numériques Mathematisches Modell Differential equations Numerical solutions Differential equations, Partial Numerical solutions Pattern formation (Physical sciences) Mathematical models Strukturbildung Nichtlineare Differentialgleichung Ordnung n Physikalisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009514331&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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