Benoit Perthame 

Transport Equations in Biology

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Transport Equations in Biology

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 models 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 observation leading to kinetic, parabolic or hyperbolic equations.

Produktinformation
  • Verlag: Birkhäuser
  • 2007
  • Ausstattung/Bilder: 2007. 208 p.
  • Seitenzahl: 212
  • Frontiers in Mathematics
  • Best.Nr. des Verlages: 11791447
  • Englisch
  • Abmessung: 254mm x 178mm x 11mm
  • Gewicht: 415g
  • ISBN-13: 9783764378417
  • ISBN-10: 3764378417
  • Best.Nr.: 22375938
Benoit Perthame, Ecole Normale Supérieure, Paris, France

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Inhaltsangabe

- 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.