A well-posedness result for a system of cross-diffusion equations

2020/11/18 by Seis, Christian, Winkler, Dominik · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.09186

Abstract

This work's major intention is the investigation of the well-posedness of certain cross-diffusion equations in the class of bounded functions. More precisely, we show existence, uniqueness and stability of bounded weak solutions under the assumption that the system has a dominant linear diffusion. As an application, we provide a new well-posedness theory for a cross-diffusion system that originates from a hopping model with size exclusions. Our approach is based on a fixed point argument in a function space that is induced by suitable Carleson-type measures.

Cited by

• Weak-strong uniqueness for general cross-diffusion systems with volume filling

Related

• Companion paper for Well posedness of general cross-diffusion systems
• Uniqueness and Regularity of Unbounded Weak Solutions to a Class of Cross Diffusion Systems
• Strong solutions and weak-strong stability in a system of cross-diffusion equations
• Local and Global Existence of Strong Solutions to Large Cross Diffusion Systems
• Global well-posedness of a conservative relaxed cross diffusion system