Strong solutions and weak-strong stability in a system of cross-diffusion equations

2018/12/27 by Berendsen, Judith, Burger, Martin, Ehrlacher, Virginie +1 · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.10711

Abstract

Proving the uniqueness of solutions to multi-species cross-diffusion systems is a difficult task in the general case, and there exist very few results in this direction. In this work, we study a particular system with zero-flux boundary conditions for which the existence of a weak solution has been proven in [Ehrlacher2017]. Under additional assumptions on the value of the cross-diffusion coefficients, we are able to show the existence and uniqueness of strong solutions. The proof relies on the use of an appropriate approximation and a fixed-point argument. In addition, a weak-strong stability result is obtained for this system in dimension one.

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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