Matched Asymptotic Expansions in Reaction-Diffusion Theory [Hardcover]

This volume contains a wealth of results and methodologies applicable to a wide range of problems arising in reaction-diffusion theory. It can be viewed both as a handbook, and as a detailed description of the methodology. The authors present new methods based on matched asymptotic expansions.

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 221.- C Analysis of Boundary Value Problem (8.76)(8.78).- D Analysis of Boundary Value Problem (8.90)(8.92).- References.

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)

Presents completely new methodologies, based on matched asymptotic expansions

Can be used both as a handbook and as a detailed description of the methodologies

This is a mathematical monograph in Reaction Diffusion Theory. It presents new methods, which will be of interest to those researching in Reaction Diffusion theory, and to those applyilCÜ