Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions

Abstract

We prove the existence of global strong solutions to the triangular Shigesada-Kawasaki-Teramoto (SKT) cross-diffusion system with Lokta-Volterra reaction terms in three dimensions. A key part is the independent careful study of the parabolic equation $a{\partial }_{t}w-\Delta w=f$ with a rough coefficient $a$, homogeneous Neumann boundary conditions, and the special assumption ${\partial }_{t}w\ge 0$. By the same method, we obtain estimates for solutions to reaction-diffusion systems modelling reversible chemistry.

arXiv comment32 pages; Previously this version appeared as arXiv:2507.19512 which was submitted as a new work by accident