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

TL;DR

This paper analyzes a complex degenerate parabolic system modeling cell behavior in intestinal crypts, establishing the existence of weak solutions through regularization and BV estimates.

Contribution

It introduces a novel mathematical framework for modeling cell dynamics in crypts with reaction-cross-diffusion equations and proves existence of solutions.

Findings

Established uniform BV estimates for the regularized system

Proved existence of weak solutions via limit passage

Provided a rigorous mathematical foundation for cell dynamics modeling

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.