Matched Asymptotic Expansions In Reaction - Diffusion Theory contains a wealth of results and methodologies applicable to a wide range of problems arising in reaction-diffusion theory.

The first part of the book is concerned with obtaining the complete structure of the large-time solution of scalar reaction diffusion equations, and systems of reaction-diffusion equations. In both cases, they are of the Fisher-Kolmogorov type, which exhibit the formation of permanent form travelling wave structures. Patticular attention is focused on determining the wave speed and the asymptotic correction to the wave speed.

The second part is concerned with the analysis of a class of singular (in the sense that the nonlinearities are not Lipschitz continuous) reaction-diffusion equations. These equations can display a wide variety of behaviours, including permanent form travelling waves, which are excitable (rather than of Fisher-Kolmogorov type).

In this detailed analysis, use is made of the method of matched asymptotic expansions, dynamical systems theory, and comparison theorems, which provide a powerful combination of techniques for the detailed analysis of this broad class of reaction-diffusion equations.

The monograph can be viewed both as a handbook, and as a detailed description of the methodology; and researchers in reaction-diffusion theory, as well as scientists applying reaction-diffusion theory to such areas as chemical kinetics, biological systems, epidemiology and population dynamics will find it a popular addition to the literature.

Content - Part I The Evolution of Travelling Waves in Scalar Fisher-Kolmogorov Equations, 1 Introduction, 2 Generalized Fisher Nonlinearity, 3 mth-Order (m > 1) Fisher Nonlinearity: Initial Data with Exponential Decay Rates or Compact Support, 4 mth-Order (m > 1) Fisher Nonlinearity: Initial Data with Algebraic Decay Rates, 5 Extension to Systems of Fisher-Kolmogorov Equations, Example: A Simple Model for an Ionic Autocatalytic System, 6 Introduction, 7 Permanent Form Travelling Waves (PTWs), 8 The Initial-Boundary Value Problem, 9 Asymptotic Solution of IBVP as t → 0 for 0 < x < : Initial Data with Exponential or Algebraic Decay Rates, 10 Extension to the System of Singular Reaction-Diffusion Equations, A Construction of a Global Nonnegative Solution to the Scalar Equation w_t = w_xx + u*wⁿ, B Asymptotic Solutions to the Eigenvalue Problem (8.68)-(8.71) as m → 0⁺ and m → 1^-, C Analysis of Boundary Value Problem (8.76)-(8.78), D Analysis of Boundary Value Problem (8.90)-(8.92), References, Index