Well-posedness of a cross-diffusion population model with nonlocal diffusion
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866917573275156480 |
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| author | Galiano, Gonzalo Velasco, Julián |
| author_facet | Galiano, Gonzalo Velasco, Julián |
| contents | We prove the existence and uniqueness of solution of a nonlocal cross-diffusion competitive population model for two species. The model may be considered as a version, or even an approximation, of the paradigmatic Shigesada-Kawasaki-Teramoto cross-diffusion model, in which the usual diffusion differential operator is replaced by an integral diffusion operator. The proof of existence of solutions is based on a compactness argument, while the uniqueness of solution is achieved through a duality technique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_04004 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Well-posedness of a cross-diffusion population model with nonlocal diffusion Galiano, Gonzalo Velasco, Julián Analysis of PDEs We prove the existence and uniqueness of solution of a nonlocal cross-diffusion competitive population model for two species. The model may be considered as a version, or even an approximation, of the paradigmatic Shigesada-Kawasaki-Teramoto cross-diffusion model, in which the usual diffusion differential operator is replaced by an integral diffusion operator. The proof of existence of solutions is based on a compactness argument, while the uniqueness of solution is achieved through a duality technique. |
| title | Well-posedness of a cross-diffusion population model with nonlocal diffusion |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1905.04004 |