Numerical Bifurcation Analysis for Reaction-Diffusion Equations

  • Zhen Mei

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 28)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Zhen Mei
    Pages 1-6
  3. Zhen Mei
    Pages 85-100
  4. Zhen Mei
    Pages 101-127
  5. Zhen Mei
    Pages 129-150
  6. Zhen Mei
    Pages 231-254
  7. Zhen Mei
    Pages 255-281
  8. Zhen Mei
    Pages 283-303
  9. Zhen Mei
    Pages 305-329
  10. Back Matter
    Pages 389-414

About this book

Introduction

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.

Keywords

Numerics Numerik Reaktion-Diffusionsgleichungen Verzweigung bifurcation calculus differential equation numerical analysis reaction-diffusion equations

Authors and affiliations

  • Zhen Mei
    • 1
  1. 1.Department of MathematicsUniversity of MarburgMarburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04177-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08669-4
  • Online ISBN 978-3-662-04177-2
  • Series Print ISSN 0179-3632
  • About this book
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