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We prove that, under a suitable rescaling of the integrable kernel definingthe nonlocal diffusion terms, the corresponding sequence of solutions of theShigesada-Kawasaki-Teramoto nonlocal cross-diffusion problem converges to asolution of the usual problem with local diffusion. In particular, the resultmay be regarded as a new proof of existence of solutions for the localdiffusion problem.

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