3 papers
math.AP2026
Interfaces and non-uniqueness in a cross-diffusion system with independent drifts
Charles Elbar, Guy Parker
We study a one-dimensional cross-diffusion system of two populations. Their densities are diffused with a common pressure that depends on the total density, but are transported by…
math.AP2026
Existence Theory for a Cross-Diffusion System with Independent Drifts: Mixing Dynamics
Alpár R. Mészáros, Guy Parker
We consider a cross-diffusion system for which the diffusion of each species is governed solely by the aggregate density through a pressure law of logarithmic or fast diffusion typ…
math.AP2025
On a Cross-Diffusion System with Independent Drifts and no Self-Diffusion: The Existence of Totally Mixed Solutions
Alpár R. Mészáros, Guy Parker
We establish the global existence of weak solutions for a two-species cross-diffusion system, set on the 1-dimensional flat torus, in which the evolution of each species is governe…