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

2025/01/12 by Chen, Xiuqing, Du, Bang · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.06821

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.

Cited by

• Weak-strong uniqueness for general cross-diffusion systems with volume filling
• Stability and uniqueness of bounded weak solutions to triangular degenerate cross-diffusion systems

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• Weak-strong uniqueness for a class of degenerate parabolic cross-diffusion systems
• Strong solutions and weak-strong stability in a system of cross-diffusion equations