Age-dependent equations with non-linear diffusion

TL;DR

This paper studies the mathematical well-posedness of age-structured population models with complex non-linear and non-local diffusion and boundary conditions, providing an abstract framework with illustrative examples.

Contribution

It introduces a novel abstract approach to handle non-linear, non-local diffusion and boundary conditions in age-structured population models.

Findings

Established well-posedness results for the models.

Demonstrated the approach with concrete examples.

Abstract

We consider the well-posedness of models involving age structure and non-linear diffusion. Such problems arise in the study of population dynamics. It is shown how diffusion and age boundary conditions can be treated that depend non-linearly and possibly non-locally on the density itself. The abstract approach is depicted with examples.