Matched Asymptotic Expansions in Reaction-Diffusion Theory

Inbunden, Engelska, 2003

AvJ.A. Leach,D.J. Needham,J. a. Leach,D. J. Needham,John Leach,David Needham,J A Leach,D J Needham

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This volume contains a wealth of results and methodologies applicable to a wide range of problems arising in reaction-diffusion theory. The first part is concerned with obtaining the complete structure of the large-time solution of scalar reaction diffusion equations, and systems of reaction-diffusion equations. The second part is concerned with the analysis of a class of singular reaction-diffusion equations. 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. Researchers in reaction-diffusion theory, and 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.

Produktinformation

Utgivningsdatum2003-12-12
Mått155 x 235 x 19 mm
Vikt550 g
FormatInbunden
SpråkEngelska
SerieSpringer Monographs in Mathematics
Antal sidor290
Upplaga2004
FörlagSpringer London Ltd
ISBN9781852337674

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Beräkning och matematisk analys inom Naturvetenskap och teknik

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)