Shock Waves and Reaction—Diffusion Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer US
1983
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
258 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | . . . the progress of physics will to a large extent depend on the progress of nonlinear mathematics, of methods to solve nonlinear equations . . . and therefore we can learn by comparing different nonlinear problems. WERNER HEISENBERG I undertook to write this book for two reasons. First, I wanted to make easily available the basics of both the theory of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by C. Conley. These important subjects seem difficult to learn since the results are scattered throughout the research journals. 1 Second, I feel that there is a need to present the modern methods and ideas in these fields to a wider audience than just mathematicians. Thus, the book has some rather sophisticated aspects to it, as well as certain textbook aspects. The latter serve to explain, somewhat, the reason that a book with the title Shock Waves and Reaction-Diffusion Equations has the first nine chapters devoted to linear partial differential equations. More precisely, I have found from my classroom experience that it is far easier to grasp the subtleties of nonlinear partial differential equations after one has an understanding of the basic notions in the linear theory. This book is divided into four main parts: linear theory, reactiondiffusion equations, shock wave theory, and the Conley index, in that order. Thus, the text begins with a discussion of ill-posed problems |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9781468401523 9781468401547 |
| DOI: | 10.1007/978-1-4684-0152-3 |
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Datensatz im Suchindex
| _version_ | 1805079046693847040 |
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| adam_text | |
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| author | Smoller, Joel |
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| dewey-full | 530.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1 |
| dewey-search | 530.1 |
| dewey-sort | 3530.1 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1007/978-1-4684-0152-3 |
| format | Electronic eBook |
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| isbn | 9781468401523 9781468401547 |
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| publishDate | 1983 |
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| series | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| spelling | Smoller, Joel Verfasser aut Shock Waves and Reaction—Diffusion Equations by Joel Smoller New York, NY Springer US 1983 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 258 . . . the progress of physics will to a large extent depend on the progress of nonlinear mathematics, of methods to solve nonlinear equations . . . and therefore we can learn by comparing different nonlinear problems. WERNER HEISENBERG I undertook to write this book for two reasons. First, I wanted to make easily available the basics of both the theory of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by C. Conley. These important subjects seem difficult to learn since the results are scattered throughout the research journals. 1 Second, I feel that there is a need to present the modern methods and ideas in these fields to a wider audience than just mathematicians. Thus, the book has some rather sophisticated aspects to it, as well as certain textbook aspects. The latter serve to explain, somewhat, the reason that a book with the title Shock Waves and Reaction-Diffusion Equations has the first nine chapters devoted to linear partial differential equations. More precisely, I have found from my classroom experience that it is far easier to grasp the subtleties of nonlinear partial differential equations after one has an understanding of the basic notions in the linear theory. This book is divided into four main parts: linear theory, reactiondiffusion equations, shock wave theory, and the Conley index, in that order. Thus, the text begins with a discussion of ill-posed problems Physics Acoustics Theoretical, Mathematical and Computational Physics Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Druckwelle (DE-588)4150776-9 gnd rswk-swf Diffusion (DE-588)4012277-3 gnd rswk-swf Diffusionsgleichung (DE-588)4149816-1 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd rswk-swf Stoßwelle (DE-588)4057760-0 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift gnd-content Stoßwelle (DE-588)4057760-0 s Reaktions-Diffusionsgleichung (DE-588)4323967-5 s 2\p DE-604 Diffusionsgleichung (DE-588)4149816-1 s 3\p DE-604 Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s 4\p DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s 5\p DE-604 Druckwelle (DE-588)4150776-9 s 6\p DE-604 Diffusion (DE-588)4012277-3 s 7\p DE-604 Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 258 (DE-604)BV049758308 258 https://doi.org/10.1007/978-1-4684-0152-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 7\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Smoller, Joel Shock Waves and Reaction—Diffusion Equations Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics Physics Acoustics Theoretical, Mathematical and Computational Physics Partielle Differentialgleichung (DE-588)4044779-0 gnd Druckwelle (DE-588)4150776-9 gnd Diffusion (DE-588)4012277-3 gnd Diffusionsgleichung (DE-588)4149816-1 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Stoßwelle (DE-588)4057760-0 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4150776-9 (DE-588)4012277-3 (DE-588)4149816-1 (DE-588)4128900-6 (DE-588)4323967-5 (DE-588)4057760-0 (DE-588)1071861417 |
| title | 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 by Joel Smoller |
| title_fullStr | Shock Waves and Reaction—Diffusion Equations by Joel Smoller |
| title_full_unstemmed | Shock Waves and Reaction—Diffusion Equations by Joel Smoller |
| title_short | Shock Waves and Reaction—Diffusion Equations |
| title_sort | shock waves and reaction diffusion equations |
| topic | Physics Acoustics Theoretical, Mathematical and Computational Physics Partielle Differentialgleichung (DE-588)4044779-0 gnd Druckwelle (DE-588)4150776-9 gnd Diffusion (DE-588)4012277-3 gnd Diffusionsgleichung (DE-588)4149816-1 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Stoßwelle (DE-588)4057760-0 gnd |
| topic_facet | Physics Acoustics Theoretical, Mathematical and Computational Physics Partielle Differentialgleichung Druckwelle Diffusion Diffusionsgleichung Nichtlineare partielle Differentialgleichung Reaktions-Diffusionsgleichung Stoßwelle Konferenzschrift |
| url | https://doi.org/10.1007/978-1-4684-0152-3 |
| volume_link | (DE-604)BV049758308 |
| work_keys_str_mv | AT smollerjoel shockwavesandreactiondiffusionequations |