On a nonlinear flux--limited equation arising in the transport of morphogens

TL;DR

This paper investigates the existence and uniqueness of entropy solutions for a nonlinear flux-limited diffusion system inspired by biological morphogen transport, highlighting its hyperbolic-like behavior rather than parabolic.

Contribution

It introduces a mathematical framework for analyzing a flux-limited diffusion model related to morphogen transport, emphasizing the hyperbolic nature of the problem.

Findings

Existence of entropy solutions established

Uniqueness of solutions proven

The model behaves more like a hyperbolic system

Abstract

Motivated by a mathematical model for the transport of morphogenes in biological systems, we study existence and uniqueness of entropy solutions for a mixed initial-boundary value problem associated with a nonlinear flux--limited diffusion system. From a mathematical point of view the problem behaves more as an hyperbolic system that a parabolic one.