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arXiv · 2110.10636

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

Gonzalo Galiano·Julián Velasco
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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.

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Gonzalo Galiano, Julián Velasco. 2021-10-20. Convergence of solutions of a rescaled evolution nonlocal cross-diffusion problem to its local diffusion counterpart. https://doi.org/10.1007/s13398-022-01231-7

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