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Matched Asymptotic Expansions in Reaction-Diffusion Theory

  • Book
  • © 2004

Overview

Authors:
  1. J. A. Leach

    1. Department of Mathematics, The University of Reading, Reading, UK

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    You can also search for this author in PubMed   Google Scholar

  2. D. J. Needham

    1. Department of Mathematics, The University of Reading, Reading, UK

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    You can also search for this author in PubMed   Google Scholar

  • Presents completely new methodologies, based on matched asymptotic expansions
  • Can be used both as a handbook and as a detailed description of the methodologies
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-X
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  2. The Evolution of Travelling Waves in Scalar Fisher-Kolmogorov Equations

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • J. A. Leach, D. J. Needham
      Pages 3-13

    3. Generalized Fisher Nonlinearity

      • J. A. Leach, D. J. Needham
      Pages 15-37

    4. mth-Order (m > 1) Fisher Nonlinearity: Initial Data with Exponential Decay Rates or Compact Support

      • J. A. Leach, D. J. Needham
      Pages 39-73

    5. mth-Order (m > 1) Fisher Nonlinearity: Initial Data with Algebraic Decay Rates

      • J. A. Leach, D. J. Needham
      Pages 75-109

    6. Extension to Systems of Fisher-Kolmogorov Equations. Example: A Simple Model for an Ionic Autocatalytic System

      • J. A. Leach, D. J. Needham
      Pages 111-147

  3. The Analysis of a Class of Singular Scalar Reaction-Diffusion Equations

    1. Front Matter

      Pages 149-149
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    2. Introduction

      • J. A. Leach, D. J. Needham
      Pages 151-154

    3. Permanent Form Travelling Waves (PTWs)

      • J. A. Leach, D. J. Needham
      Pages 155-176

    4. The Initial-Boundary Value Problem

      • J. A. Leach, D. J. Needham
      Pages 177-211

    5. Asymptotic Solution of IBVP as t → 0 for 0 ≤ x < ∞: Initial Data with Exponential or Algebraic Decay Rates

      • J. A. Leach, D. J. Needham
      Pages 213-220

    6. Extension to the System of Singular Reaction-Diffusion Equations

      • J. A. Leach, D. J. Needham
      Pages 221-269

  4. Back Matter

    Pages 271-290
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Keywords

Reviews

From the reviews of the first edition:

"The book contains useful information on the topic, especially precise (and non-standard) asymptotic expansions in different regions collected with the help of the MAE-s into the complete characterization of the solutions to the nonlinear problems in consideration. The book is warmly recommended to specialists in ODE-s, PDE-s, researchers in reaction-diffusion theory, physicists, engineers and to students with basic knowledge on parabolic equations." (Jeno Hegedus, Acta Scientiarum Mathematicarum, Vol. 72, 2006)

Authors and Affiliations

  • Department of Mathematics, The University of Reading, Reading, UK

    J. A. Leach, D. J. Needham

Bibliographic Information

  • Book Title: Matched Asymptotic Expansions in Reaction-Diffusion Theory

  • Authors: J. A. Leach, D. J. Needham

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-0-85729-396-1

  • Publisher: Springer London

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag London 2004

  • Hardcover ISBN: 978-1-85233-767-4Published: 12 December 2003

  • Softcover ISBN: 978-1-4471-1054-5Published: 23 October 2012

  • eBook ISBN: 978-0-85729-396-1Published: 06 December 2012

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: X, 290

  • Topics: Approximations and Expansions, Partial Differential Equations

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