Uniqueness of Weak Solutions to One-Dimensional Doubly Degenerate Cross-Diffusion System

TL;DR

This paper proves the uniqueness of global weak solutions for a one-dimensional doubly degenerate cross-diffusion system modeling bacterial populations, using an anti-derivative approach to establish the result.

Contribution

It introduces a novel method employing anti-derivatives to prove uniqueness for a complex cross-diffusion system with degeneracy.

Findings

Uniqueness of weak solutions is established.

Method applicable to similar degenerate systems.

Provides insights into bacterial population dynamics.

Abstract

The uniqueness of global weak solutions to one-dimensional doubly degenerate cross-diffusion system is shown. The equations model the evolution of feeding bacterial populations in a malnourished environment. The key idea of the proof is applying anti-derivative of the sum of weak solutions to the system.