Parabolic models in population dynamics

Nicolas Vauchelet

Summary :

Parabolic partial differential equations are now widely used to model the time and spatial dynamics of a population or a colony of cells. The aim of this course is to present why such models are interesting to model some biological phenomena and to show how to analyze them from a mathematical point a view. In particular, we focus on deriving qualitative properties of the solutions, which are relevant for applications. More precisely, we are interesting in invasion phenomena, well described by traveling waves in reaction-diffusion equation, in long time behavior of solutions, their stability, and Turing instabilities which can occur in some systems.