A note on the uniqueness of weak solutions to a class of cross-diffusion systems

2017/06/27 by Chen, Xiuqing, Jüngel, Ansgar · 2 citations
#35A02 #35K51 #35K55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.08812

Abstract

The uniqueness of bounded weak solutions to strongly coupled parabolic equations in a bounded domain with no-flux boundary conditions is shown. The equations include cross-diffusion and drift terms and are coupled selfconsistently to the Poisson equation. The model class contains special cases of the Maxwell-Stefan equations for gas mixtures, generalized Shigesada-Kawasaki-Teramoto equations for population dynamics, and volume-filling models for ion transport. The uniqueness proof is based on a combination of the H^-1 technique and the entropy method of Gajewski.

Cited by

• Stability of non-conservative cross diffusion model and approximation by stochastic particle systems
• Stability and uniqueness of bounded weak solutions to triangular degenerate cross-diffusion systems

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