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

TL;DR

This paper establishes well-posedness for a class of cross-diffusion equations with dominant linear diffusion, using fixed point methods in Carleson measure spaces, and applies it to a size-exclusion hopping model.

Contribution

It provides a new well-posedness theory for cross-diffusion systems with dominant linear diffusion, including a novel application to a size-exclusion hopping model.

Findings

Existence, uniqueness, and stability of bounded weak solutions.

Application to a cross-diffusion system from a hopping model with size exclusions.

Use of fixed point argument in Carleson-type measure spaces.

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.