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Elliptic Partial Differential Equations

Volume 2: Reaction-Diffusion Equations

  • Book
  • © 2014

Overview

Authors:
  1. Vitaly Volpert

    1. Institut Camille Jordan, CNRS, Université Claude Bernard Lyon 1, Villeurbanne, France

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  • Offers a systematic investigation of reaction-diffusion equations including existence, stability and bifurcations of solutions
  • Presents numerous examples and applications from population dynamics, chemical physics, biomedical models
  • Sequel to successful first volume

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

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Table of contents (10 chapters)

  1. Front Matter

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

    1. Front Matter

      Pages 1-1
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    2. Reaction-diffusion Processes, Models and Applications

      • Vitaly Volpert
      Pages 3-78

    3. Methods of Analysis

      • Vitaly Volpert
      Pages 79-121

    4. Reaction-diffusion Problems in Bounded Domains

      • Vitaly Volpert
      Pages 123-200

    5. Reaction-diffusion Problems on the Whole Axis

      • Vitaly Volpert
      Pages 201-324

  3. Reaction-diffusion Waves in Cylinders

    1. Front Matter

      Pages 325-326
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    2. Monotone Systems

      • Vitaly Volpert
      Pages 327-390

    3. Reaction-diffusion Problems with Convection

      • Vitaly Volpert
      Pages 391-451

    4. Reaction-diffusion Systems with Different Transport Coefficients

      • Vitaly Volpert
      Pages 453-490

    5. Nonlinear Boundary Conditions

      • Vitaly Volpert
      Pages 491-517

  4. Nonlocal and Multi-scale Models

    1. Front Matter

      Pages 519-519
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    2. Nonlocal Reaction-diffusion Equations

      • Vitaly Volpert
      Pages 521-626

    3. Multi-scale Models in Biology

      • Vitaly Volpert
      Pages 627-696

  5. Back Matter

    Pages 697-784
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Keywords

About this book

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. 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.

Reviews

“This volume is concerned with the mathematical analysis of reaction-diffusion partial differential equations in relationship with their multiple applications. … This volume is useful to researchers in pure and applied nonlinear analysis and to graduate students in mathematics and mathematical physics.” (Vicenţiu D. Rădulescu, Mathematical Reviews, November, 2015)

Authors and Affiliations

  • Institut Camille Jordan, CNRS, Université Claude Bernard Lyon 1, Villeurbanne, France

    Vitaly Volpert

About the author

Vitaly Volpert started his scientific career in Russia and continued it in the USA and in France. He works on partial differential equations and on mathematical modelling in chemical physics, biology and medicine. He is an author of more than 200 scientific publications including three monographs.

Bibliographic Information

  • Book Title: Elliptic Partial Differential Equations

  • Book Subtitle: Volume 2: Reaction-Diffusion Equations

  • Authors: Vitaly Volpert

  • Series Title: Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-0813-2

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Basel 2014

  • Hardcover ISBN: 978-3-0348-0812-5Published: 20 May 2014

  • eBook ISBN: 978-3-0348-0813-2Published: 10 May 2014

  • Series ISSN: 1017-0480

  • Series E-ISSN: 2296-4886

  • Edition Number: 1

  • Number of Pages: XVIII, 784

  • Number of Illustrations: 27 b/w illustrations, 17 illustrations in colour

  • Topics: Partial Differential Equations

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