Convergence of solutions of a rescaled evolution nonlocal cross-diffusion problem to its local diffusion counterpart

Abstract

We prove that, under a suitable rescaling of the integrable kernel defining the nonlocal diffusion terms, the corresponding sequence of solutions of the Shigesada-Kawasaki-Teramoto nonlocal cross-diffusion problem converges to a solution of the usual problem with local diffusion. In particular, the result may be regarded as a new proof of existence of solutions for the local diffusion problem.

References in corpus (4)

• Numerical methods for nonlocal and fractional models
• The boundedness-by-entropy principle for cross-diffusion systems
• A cookbook for finite element methods for nonlocal problems, including quadrature rules and approximate Euclidean balls
• Error analysis of some nonlocal diffusion discretization schemes