Helge Dietert (Université Paris Cité et Sorbonne Université): Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions

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 \(\partial_tw \ge 0\). By the same method, we obtain estimates for solutions to reaction-diffusion systems modelling reversible chemistry.