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Elliptic Partial Differential Equations

Volume 2: Reaction-Diffusion Equations

  • Vitaly Volpert

Part of the Monographs in Mathematics book series (MMA, volume 104)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Introduction to the Theory of Reaction-diffusion Equations

    1. Front Matter
      Pages 1-1
    2. Vitaly Volpert
      Pages 79-121
    3. Vitaly Volpert
      Pages 123-200
    4. Vitaly Volpert
      Pages 201-324
  3. Reaction-diffusion Waves in Cylinders

    1. Front Matter
      Pages 325-326
    2. Vitaly Volpert
      Pages 327-390
    3. Vitaly Volpert
      Pages 391-451
    4. Vitaly Volpert
      Pages 491-517
  4. Nonlocal and Multi-scale Models

    1. Front Matter
      Pages 519-519
    2. Vitaly Volpert
      Pages 521-626
    3. Vitaly Volpert
      Pages 627-696
  5. Back Matter
    Pages 697-784

About this book

Introduction

If we had to formulate in one sentence what this book is about it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Mathematical anaylsis of reaction-diffusion equations will be based on the theory of Fredholm operators presented in the first volume. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equations and new topics such as nonlocal equations and multi-scale models in biology will be considered.

Keywords

bifurcations of solutions classical theory existence of solutions population dynamics reaction-diffusion equations stability of solutions

Authors and affiliations

  • Vitaly Volpert
    • 1
  1. 1.Institut Camille Jordan, CNRSUniversité Claude Bernard Lyon 1VilleurbanneFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0813-2
  • Copyright Information Springer Basel 2014
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0812-5
  • Online ISBN 978-3-0348-0813-2
  • Series Print ISSN 1017-0480
  • Series Online ISSN 2296-4886
  • Buy this book on publisher's site