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| HAL : hal-00462460, version 1 |
| Fiche détaillée |  Récupérer au format |
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| A fully adaptive numerical approximation for a two-dimensional epidemic model with nonlinear cross-diffusion |
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| Berres Stefan 1Ricardo Ruiz Baier 2 |
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| (08/03/2010) |
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| An epidemic model is formulated by a reaction-diffusion system where the spatial pattern formation is driven by cross-diffusion. Whereas the reaction terms describe the local dynamics of susceptible and infected species, the diffusion terms account for the spatial distribution dynamics. For both self-diffusion and cross-diffusion nonlinear constitutive assumptions are suggested. To simulate the pattern formation two finite volume formulations are proposed, which employ a conservative and a non-conservative discretization, respectively. An efficient simulation is obtained by a fully adaptive multiresolution strategy. Numerical examples illustrate the impact of the cross-diffusion on the pattern formation. |
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| 1 : | Departamento de Ciencias Matem\'{a}tica y F\'{\i}sica |
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Universidad Católica de Temuco |
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| 2 : | Ecole Polytechnique Fédérale de Lausanne (EPFL) |
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École Polytechnique Fédérale de Lausanne |
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| Domaine | : | Mathématiques/Analyse numérique Science non linéaire/Formation de Structures et Solitons |
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| Epidemic model – reaction-diffusion equation – cross-diffusion – fully adaptive multiresolution |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00462460, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00462460 | |
| oai:hal.archives-ouvertes.fr:hal-00462460 | |
| Contributeur : Ricardo Ruiz Baier | |
| Soumis le : Mardi 9 Mars 2010, 17:38:42 | |
| Dernière modification le : Mercredi 10 Mars 2010, 21:17:41 | |
