zbMATH — the first resource for mathematics

Transport equations in biology. (English) Zbl 1185.92006
Frontiers in Mathematics. Basel: Birkhäuser (ISBN 3-7643-7841-7/pbk). ix, 198 p. (2007).
Publisher’s description: 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.

92C05 Biophysics
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92C17 Cell movement (chemotaxis, etc.)