Uniqueness result for an age-dependent reaction-diffusion problem

Abstract

This paper is concerned with an age-structured model in population dynamics. We investigate the uniqueness of solution for this type of nonlinear reaction-diffusion problem when the source term depends on the density, indicating the presence of, for example, mortality and reaction processes. Our result shows that in a spatial environment, if two population densities obey the same evolution equation and possess the same terminal data of time and age, then their distributions must coincide therein.