Overview
- Authors:
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Jacek Banasiak
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School of Mathematics, Statistics and Computer Science/Institute of Mathematics, University of KwaZulu-Natal, South Africa/Technical University of Łódź, Poland, Durban, South Africa
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Mirosław Lachowicz
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Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland
- Unified approach to singular perturbed problems
- Applications and examples to mathematical biology
- Chapters are arranged according to the mathematical complexity
- Includes supplementary material: sn.pub/extras
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Table of contents (9 chapters)
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- Jacek Banasiak, Mirosław Lachowicz
Pages 1-44
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- Jacek Banasiak, Mirosław Lachowicz
Pages 45-76
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- Jacek Banasiak, Mirosław Lachowicz
Pages 77-104
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- Jacek Banasiak, Mirosław Lachowicz
Pages 105-141
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- Jacek Banasiak, Mirosław Lachowicz
Pages 143-172
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- Jacek Banasiak, Mirosław Lachowicz
Pages 173-194
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- Jacek Banasiak, Mirosław Lachowicz
Pages 195-221
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- Jacek Banasiak, Mirosław Lachowicz
Pages 223-270
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- Jacek Banasiak, Mirosław Lachowicz
Pages 271-272
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Back Matter
Pages 273-285
About this book
This monograph presents new tools for modeling multiscale biological processes. Natural processes are usually driven by mechanisms widely differing from each other in the time or space scale at which they operate and thus should be described by appropriate multiscale models. However, looking at all such scales simultaneously is often infeasible, costly, and provides information that is redundant for a particular application. Hence, there has been a growing interest in providing a more focused description of multiscale processes by aggregating variables in a way that is relevant to the purpose at hand and preserves the salient features of the dynamics. Many ad hoc methods have been devised, and the aim of this book is to present a systematic way of deriving the so-called limit equations for such aggregated variables and ensuring that the coefficients of these equations encapsulate the relevant information from the discarded levels of description. Since any approximation is only valid if an estimate of the incurred error is available, the tools the authors describe allow for proving that the solutions to the original multiscale family of equations converge to the solution of the limit equation if the relevant parameter converges to its critical value. The chapters are arranged according to the mathematical complexity of the analysis, from systems of ordinary linear differential equations, through nonlinear ordinary differential equations, to linear and nonlinear partial differential equations. Many chapters begin with a survey of mathematical techniques needed for the analysis. All problems discussed in this book belong to the class of singularly perturbed problems; that is, problems in which the structure of the limit equation is significantly different from that of the multiscale model. Such problems appear in all areas of science and can be attacked using many techniques. Methods of Small Parameter in Mathematical Biology will appeal to seniorundergraduate and graduate students in applied and biomathematics, as well as researchers specializing in differential equations and asymptotic analysis.
Authors and Affiliations
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School of Mathematics, Statistics and Computer Science/Institute of Mathematics, University of KwaZulu-Natal, South Africa/Technical University of Łódź, Poland, Durban, South Africa
Jacek Banasiak
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Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland
Mirosław Lachowicz
