Global solutions of reaction-diffusion systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Tokyo
Springer-Verlag
1984
|
| Series: | Lecture notes in mathematics
1072 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | V, 216 Seiten |
| ISBN: | 3540133658 0387133658 |
Staff View
MARC
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| 245 | 1 | 0 | |a Global solutions of reaction-diffusion systems |c Franz Rothe |
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| 490 | 1 | |a Lecture notes in mathematics |v 1072 | |
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| 650 | 7 | |a Équations différentielles paraboliques - Solutions numériques |2 ram | |
| 650 | 4 | |a Biomathematics | |
| 650 | 4 | |a Reaction-diffusion equations |x Numerical solutions | |
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Record in the Search Index
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| adam_text | Contents
Introduction 1
Part I Existence and A Priori Estimates for
Reaction Diffusion Equations 5
Basic Notations and Definitions 11
Theorem 1 (Existence of mild solutions) 32
Theorem 2 (Existence of mild solutions in the case of
minimal regularity of the initial data) 33
Corollary of Theorem 1 (Uniqueness and maximality) 54
Theorem 3 (Existence results exploiting a priori estimates) 57
Theorem 4 (Global existence and global a priori estimates) 67
Theorem 5 (Results on the behavior of the solution at a finite
maximal existence time, which are available without
global Lipschitz condition) . . 76
Theorem 6 (Global existence and uniform a priori estimates
in the case without global Lipschitz condition) 91
Theorem 7 (Stronger results for sublinear equations using
only weak primary a priori estimates) 102
Part II Some Examples of Reaction Diffusion Systems
Arising in Applications 104
Review of Standard Theorems 108
Theorem 1 (Existence of mild and classical solutions) 111
Theorem 2 (Construction of global solutions for
irregular initial data) 120
Theorem 3 (Comparison of solutions by the
strong maximum principle) 123
The Gierer Meinhardt Model 126
Theorem (Globally bounded solutions for
space dimension N = 1,2,3) 126
V
The Brusselator 1 40
Theorem 1 (Globally bounded solutions for
space dimension N = 1,2,3) 140
Theorem 2 (Global solution for space dimension N = 4) 146
The FitzHugh Nagumo System 148
Theorem 1 (Global solutions for arbitrary space dimension) 149
Theorem 2 (Sufficient conditions for decay of solutions
in space dimension N 3) 154
Chemical Reactions 157
Theorem 1 (Globally bounded solutions for
space dimension N 5) 157
Theorem 2 (Asymptotic behavior by means of entropy) 167
A Nuclear Reactor Model 172
Theorem (Boundedness and convergence to equilibrium) 173
The Volterra Lotka Model 188
Theorem 1 (Boundedness and convergence to equilibrium) 189
Theorem 2 (Degenerate cases with one nondiffusing species) 190
Theorem 3 (Boundedness and convergence to equilibrium for
some generalized Volterra Lotka systems) 207
References 211
Index 215
|
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| discipline | Biologie Mathematik |
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| indexdate | 2024-07-09T15:10:28Z |
| institution | BVB |
| isbn | 3540133658 0387133658 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000125097 |
| oclc_num | 10948372 |
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| physical | V, 216 Seiten |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Springer-Verlag |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Rothe, Franz 1947- (DE-588)1011909804 aut Global solutions of reaction-diffusion systems Franz Rothe Berlin ; Heidelberg ; New York ; Tokyo Springer-Verlag 1984 V, 216 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1072 Analyse globale (Mathématiques) Biomathématiques Équations aux dérivées partielles - Solutions numériques Équations différentielles paraboliques - Solutions numériques Équations différentielles paraboliques - Solutions numériques ram Biomathematics Reaction-diffusion equations Numerical solutions Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd rswk-swf Globale Lösung (DE-588)4264389-2 gnd rswk-swf Reaktions-Diffusionsgleichung (DE-588)4323967-5 s Globale Lösung (DE-588)4264389-2 s DE-604 Lecture notes in mathematics 1072 (DE-604)BV000676446 1072 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000125097&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rothe, Franz 1947- Global solutions of reaction-diffusion systems Lecture notes in mathematics Analyse globale (Mathématiques) Biomathématiques Équations aux dérivées partielles - Solutions numériques Équations différentielles paraboliques - Solutions numériques Équations différentielles paraboliques - Solutions numériques ram Biomathematics Reaction-diffusion equations Numerical solutions Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Globale Lösung (DE-588)4264389-2 gnd |
| subject_GND | (DE-588)4323967-5 (DE-588)4264389-2 |
| title | Global solutions of reaction-diffusion systems |
| title_auth | Global solutions of reaction-diffusion systems |
| title_exact_search | Global solutions of reaction-diffusion systems |
| title_full | Global solutions of reaction-diffusion systems Franz Rothe |
| title_fullStr | Global solutions of reaction-diffusion systems Franz Rothe |
| title_full_unstemmed | Global solutions of reaction-diffusion systems Franz Rothe |
| title_short | Global solutions of reaction-diffusion systems |
| title_sort | global solutions of reaction diffusion systems |
| topic | Analyse globale (Mathématiques) Biomathématiques Équations aux dérivées partielles - Solutions numériques Équations différentielles paraboliques - Solutions numériques Équations différentielles paraboliques - Solutions numériques ram Biomathematics Reaction-diffusion equations Numerical solutions Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Globale Lösung (DE-588)4264389-2 gnd |
| topic_facet | Analyse globale (Mathématiques) Biomathématiques Équations aux dérivées partielles - Solutions numériques Équations différentielles paraboliques - Solutions numériques Biomathematics Reaction-diffusion equations Numerical solutions Reaktions-Diffusionsgleichung Globale Lösung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000125097&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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