Convergence of solutions of a rescaled evolution nonlocal cross-diffusion problem to its local diffusion counterpart
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866911764977811456 |
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| author | Galiano, Gonzalo Velasco, Julián |
| author_facet | Galiano, Gonzalo Velasco, Julián |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_10636 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Convergence of solutions of a rescaled evolution nonlocal cross-diffusion problem to its local diffusion counterpart Galiano, Gonzalo Velasco, Julián Analysis of PDEs 45K05, 35K55, 45G15 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. |
| title | Convergence of solutions of a rescaled evolution nonlocal cross-diffusion problem to its local diffusion counterpart |
| topic | Analysis of PDEs 45K05, 35K55, 45G15 |
| url | https://arxiv.org/abs/2110.10636 |