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Introduction

  • J. A. Leach
  • D. J. Needham
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

In Part I of this monograph, we develop, via the method of matched asymptotic expansions (MAE), a rational approach to obtaining the complete large-t (dimensionless time) structure of the solution to initial-boundary value problems (IBVPs) and initial value problems (IVPs) for reaction-diffusion equations of the Fisher-Kolmogorov type, which exhibit the formation of a permanent form travelling wave (PTW) structure. In particular, this approach allows the wave speed for the large-t PTW, the correction to the wave speed and the rate of convergence of the solution of the IBVP or IVP onto the PTW to be determined. This large-t structure is obtained by careful consideration of the asymptotic structures as t→ 0 (0 ≤ x < ∞) (where x is the dimensionless distance) and as x→ ∞ (tO(1)).

Keywords

Wave Front Wave Speed Propagation Speed Reaction Function Matched Asymptotic Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London 2004

Authors and Affiliations

  • J. A. Leach
    • 1
  • D. J. Needham
    • 1
  1. 1.Department of MathematicsThe University of ReadingReadingUK

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