Numerical Bifurcation Analysis for Reaction-Diffusion Equations - Couverture souple

Mei, Zhen

Couverture souple

ISBN 10 : 3642086691 ISBN 13 : 9783642086694

Editeur : Springer, 2010

Synopsis

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.

A propos du livre

Présentation de l'éditeur

This monograph is the first to provide readers with numerical tools for a systematic analysis of bifurcation problems in reaction-diffusion equations. Many examples and figures illustrate analysis of bifurcation scenario and implementation of numerical schemes. Readers will gain a thorough understanding of numerical bifurcation analysis and the necessary tools for investigating nonlinear phenomena in reaction-diffusion equations.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2010
• Langue: anglais
• ISBN 10: 3642086691
• ISBN 13: 9783642086694
• Reliure: Broché
• Nombre de pages: 432
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne