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Academic & Professional Books  Reference  Physical Sciences  Mathematics

Transport Equations in Biology

By: Benoit Perthame
198 pages, 28 illus
Transport Equations in Biology
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  • Transport Equations in Biology ISBN: 9783764378417 Paperback Dec 2007 Usually dispatched within 1-2 weeks
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About this book

This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions (long time behavior, concentration phenomena, asymptotic behavior, regularizing effects, blow-up or dispersion). Original mathematical methods described are, among others, the generalized relative entropy method - a unique method to tackle most of the problems in population biology, the description of Dirac concentration effects using a new type of Hamilton-Jacobi equations, and a general point of view on chemotaxis including various scales of description leading to kinetic, parabolic or hyperbolic equations.

Contents

Preface.- 1. From Differential Equations to Structured Population Dynamics.- 2. Adaptive Dynamics; an Asymptotic Point of View.- 3. Population Balance Equations: the Renewal Equation.- 4. Population Balance Equations: Size Structure.- 5. Cell Motion and Chemotaxis.- 6. General Mathematical Tools.- Bibliography.- Index.

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By: Benoit Perthame
198 pages, 28 illus
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