Numerical Bifurcation Analysis for Reaction-Diffusion Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2000
|
| Schriftenreihe: | Springer Series in Computational Mathematics
28 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Reaction-diffusion equations are typical mathematical models in biology, chemistry and physics. These equations often depend on various parame ters, e. g. temperature, catalyst and diffusion rate, etc. Moreover, they form normally a nonlinear dissipative system, coupled by reaction among differ ent substances. The number and stability of solutions of a reaction-diffusion system may change abruptly with variation of the control parameters. Cor respondingly we see formation of patterns in the system, for example, an onset of convection and waves in the chemical reactions. This kind of phe nomena is called bifurcation. Nonlinearity in the system makes bifurcation take place constantly in reaction-diffusion processes. Bifurcation in turn in duces uncertainty in outcome of reactions. Thus analyzing bifurcations is essential for understanding mechanism of pattern formation and nonlinear dynamics of a reaction-diffusion process. However, an analytical bifurcation analysis is possible only for exceptional cases. This book is devoted to nu merical analysis of bifurcation problems in reaction-diffusion equations. The aim is to pursue a systematic investigation of generic bifurcations and mode interactions of a dass of reaction-diffusion equations. This is realized with a combination of three mathematical approaches: numerical methods for con tinuation of solution curves and for detection and computation of bifurcation points; effective low dimensional modeling of bifurcation scenario and long time dynamics of reaction-diffusion equations; analysis of bifurcation sce nario, mode-interactions and impact of boundary conditions |
| Beschreibung: | 1 Online-Ressource (XIV, 414 p) |
| ISBN: | 9783662041772 9783642086694 |
| ISSN: | 0179-3632 |
| DOI: | 10.1007/978-3-662-04177-2 |
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Datensatz im Suchindex
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| isbn | 9783662041772 9783642086694 |
| issn | 0179-3632 |
| language | English |
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| spelling | Mei, Zhen Verfasser aut Numerical Bifurcation Analysis for Reaction-Diffusion Equations by Zhen Mei Berlin, Heidelberg Springer Berlin Heidelberg 2000 1 Online-Ressource (XIV, 414 p) txt rdacontent c rdamedia cr rdacarrier Springer Series in Computational Mathematics 28 0179-3632 Reaction-diffusion equations are typical mathematical models in biology, chemistry and physics. These equations often depend on various parame ters, e. g. temperature, catalyst and diffusion rate, etc. Moreover, they form normally a nonlinear dissipative system, coupled by reaction among differ ent substances. The number and stability of solutions of a reaction-diffusion system may change abruptly with variation of the control parameters. Cor respondingly we see formation of patterns in the system, for example, an onset of convection and waves in the chemical reactions. This kind of phe nomena is called bifurcation. Nonlinearity in the system makes bifurcation take place constantly in reaction-diffusion processes. Bifurcation in turn in duces uncertainty in outcome of reactions. Thus analyzing bifurcations is essential for understanding mechanism of pattern formation and nonlinear dynamics of a reaction-diffusion process. However, an analytical bifurcation analysis is possible only for exceptional cases. This book is devoted to nu merical analysis of bifurcation problems in reaction-diffusion equations. The aim is to pursue a systematic investigation of generic bifurcations and mode interactions of a dass of reaction-diffusion equations. This is realized with a combination of three mathematical approaches: numerical methods for con tinuation of solution curves and for detection and computation of bifurcation points; effective low dimensional modeling of bifurcation scenario and long time dynamics of reaction-diffusion equations; analysis of bifurcation sce nario, mode-interactions and impact of boundary conditions Mathematics Global analysis (Mathematics) Numerical analysis Numerical Analysis Analysis Theoretical, Mathematical and Computational Physics Mathematik Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Reaktions-Diffusionsgleichung (DE-588)4323967-5 s Verzweigung Mathematik (DE-588)4078889-1 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 https://doi.org/10.1007/978-3-662-04177-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mei, Zhen Numerical Bifurcation Analysis for Reaction-Diffusion Equations Mathematics Global analysis (Mathematics) Numerical analysis Numerical Analysis Analysis Theoretical, Mathematical and Computational Physics Mathematik Numerisches Verfahren (DE-588)4128130-5 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4323967-5 (DE-588)4078889-1 |
| title | Numerical Bifurcation Analysis for Reaction-Diffusion Equations |
| title_auth | Numerical Bifurcation Analysis for Reaction-Diffusion Equations |
| title_exact_search | Numerical Bifurcation Analysis for Reaction-Diffusion Equations |
| title_full | Numerical Bifurcation Analysis for Reaction-Diffusion Equations by Zhen Mei |
| title_fullStr | Numerical Bifurcation Analysis for Reaction-Diffusion Equations by Zhen Mei |
| title_full_unstemmed | Numerical Bifurcation Analysis for Reaction-Diffusion Equations by Zhen Mei |
| title_short | Numerical Bifurcation Analysis for Reaction-Diffusion Equations |
| title_sort | numerical bifurcation analysis for reaction diffusion equations |
| topic | Mathematics Global analysis (Mathematics) Numerical analysis Numerical Analysis Analysis Theoretical, Mathematical and Computational Physics Mathematik Numerisches Verfahren (DE-588)4128130-5 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Numerical analysis Numerical Analysis Analysis Theoretical, Mathematical and Computational Physics Mathematik Numerisches Verfahren Reaktions-Diffusionsgleichung Verzweigung Mathematik |
| url | https://doi.org/10.1007/978-3-662-04177-2 |
| work_keys_str_mv | AT meizhen numericalbifurcationanalysisforreactiondiffusionequations |