Uniqueness result for an age-dependent reaction-diffusion problem

TL;DR

This paper proves the uniqueness of solutions for an age-dependent reaction-diffusion model in population dynamics, showing that identical terminal data leads to identical population distributions in space, age, and time.

Contribution

It establishes a mathematical uniqueness result for a nonlinear age-structured reaction-diffusion equation with density-dependent source terms.

Findings

Solutions with the same terminal data are identical in the spatial and age distribution.

The result applies to models with mortality and reaction processes.

Uniqueness holds under the specified conditions for the nonlinear 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.