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. It develops appropriate mathematical tools and qualitative properties of the solutions (long time behavior, concentration phenomena, asymptotic behavior, regularizing effects, blow-up or dispersion). The book describes such original mathematical methods as 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.

Contains many original PDE problems originating in biosciences Point of view is that mathematics describes the properties of the solutions Includes supplementary material: sn.pub/extras

Inhalt
From differential equations to structured population dynamics.- Adaptive dynamics; an asymptotic point of view.- Population balance equations: the renewal equation.- Population balance equations: size structure.- Cell motion and chemotaxis.- General mathematical tools.