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＜電子ブック＞
Numerical Bifurcation Analysis for Reaction-Diffusion Equations / by Zhen Mei
(Springer Series in Computational Mathematics. ISSN:21983712 ; 28)

版	1st ed. 2000.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2000
本文言語	英語
大きさ	XIV, 414 p : online resource
著者標目	*Mei, Zhen author SpringerLink (Online service)
件　名	LCSH:Numerical analysis LCSH:Mathematical analysis LCSH:Mathematical physics FREE:Numerical Analysis FREE:Analysis FREE:Theoretical, Mathematical and Computational Physics
一般注記	1. Reaction-Diffusion Equations -- 2. Continuation Methods -- 3. Detecting and Computing Bifurcation Points -- 4. Branch Switching at Simple Bifurcation Points -- 5. Bifurcation Problems with Symmetry -- 6. Liapunov-Schmidt Method -- 7. Center Manifold Theory -- 8. A Bifurcation Function for Homoclinic Orbits -- 9. One-Dimensional Reaction-Diffusion Equations -- 10. Reaction-Diffusion Equations on a Square -- 11. Normal Forms for Hopf Bifurcations -- 12. Steady/Steady State Mode Interactions -- 13. Hopf/Steady State Mode Interactions -- 14. Homotopy of Boundary Conditions -- 15. Bifurcations along a Homotopy of BCs -- 16. A Mode Interaction on a Homotopy of BCs -- List of Figures -- List of Tables 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 HTTP:URL=https://doi.org/10.1007/978-3-662-04177-2

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