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∂t w - w = f with a rough coefficient a, homogeneous Neumann boundary conditions, and the special assumption ∂t w 0. By the same method, we obtain estimates for solutions to reaction-diffusion systems modelling reversible chemistry.
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