Analysis of a degenerate parabolic system for cell dynamics in intestinal crypts

Abstract

In this work, we study a system of degenerate parabolic equations modeling the dynamics of multiple cell populations in intestinal crypts. The model describes cell division, differentiation, and migration through a strongly coupled system of reaction-cross-diffusion equations with degenerate diffusion. By working with initial data in BV, we first consider a regularized form of the system and establish uniform BV estimates. Using these bounds, we then pass to the limit to obtain the existence of weak solutions.