Shock Waves and Reaction—Diffusion Equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1994
|
| Edition: | Second Edition |
| Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
258 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in con structing travelling waves for systems of nonlinear equations. The final section, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applicable to many interesting reaction-diffusion systems |
| Physical Description: | 1 Online-Ressource (XXIII, 634 p) |
| ISBN: | 9781461208730 9781461269298 |
| DOI: | 10.1007/978-1-4612-0873-0 |
Staff View
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Record in the Search Index
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| discipline | Mathematik |
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| edition | Second Edition |
| format | Electronic eBook |
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| indexdate | 2024-07-20T06:38:46Z |
| institution | BVB |
| isbn | 9781461208730 9781461269298 |
| language | English |
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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 1935- Verfasser (DE-588)1024209652 aut Shock Waves and Reaction—Diffusion Equations by Joel Smoller Second Edition New York, NY Springer New York 1994 1 Online-Ressource (XXIII, 634 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 258 For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in con structing travelling waves for systems of nonlinear equations. The final section, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applicable to many interesting reaction-diffusion systems Mathematics Global analysis (Mathematics) Analysis Mathematik 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/10.1007/978-1-4612-0873-0 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 1935- Shock Waves and Reaction—Diffusion Equations Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics Mathematics Global analysis (Mathematics) Analysis Mathematik 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 | Mathematics Global analysis (Mathematics) Analysis Mathematik 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 | Mathematics Global analysis (Mathematics) Analysis Mathematik Partielle Differentialgleichung Druckwelle Diffusion Diffusionsgleichung Nichtlineare partielle Differentialgleichung Reaktions-Diffusionsgleichung Stoßwelle Konferenzschrift |
| url | https://doi.org/10.1007/978-1-4612-0873-0 |
| volume_link | (DE-604)BV049758308 |
| work_keys_str_mv | AT smollerjoel shockwavesandreactiondiffusionequations |