Diffusive and nondiffusive population models

Abstract

This survey is concerned with the modeling and mathematical analysis of continuous population equations. These models describe the change of the number of species due to birth, death, spatial movements, or stage variations. Our main focus is on spatially inhomogeneous models, given by reaction-diffusion equations, but we review also age- and size-structured and time-delayed population models. Results on the existence and stability of solutions as well as their qualitative behavior are given.