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Transport Equations in Biology

Series: Frontiers in Mathematics

By: Benoit Perthame

198 pages, 28 illus

Birkhäuser Verlag

Paperback | Dec 2007 | #163880 | ISBN-13: 9783764378417
Availability: Usually dispatched within 1 week Details
NHBS Price: £49.99 $66/€57 approx

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.


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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