Weak-strong uniqueness of renormalized solutions to reaction-cross-diffusion systems

2018/05/08 by Chen, Xiuqing, Jüngel, Ansgar · 3 citations
#35A02 #35K51 #35K55 #35Q92 #92D25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.02950

Abstract

The weak-strong uniqueness for solutions to reaction-cross-diffusion systems in a bounded domain with no-flux boundary conditions is proved. The system generalizes the Shigesada-Kawasaki-Teramoto population model to an arbitrary number of species. The diffusion matrix is neither symmetric nor positive definite, but the system possesses a formal gradient-flow or entropy structure. No growth conditions on the source terms are imposed. It is shown that any renormalized solution coincides with a strong solution with the same initial data, as long as the strong solution exists. The proof is based on the evolution of the relative entropy modified by suitable cutoff functions.

Cited by

• Stability of non-conservative cross diffusion model and approximation by stochastic particle systems
• 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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