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university of Provence - Aix-Marseille I |  |
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university of Provence - Aix-Marseille I | |
| HAL: hal-00521968, version 1 |
| DOI: 10.1080/17513758.2011.568071 |
| Detailed view |  Export this paper |
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| Journal of Biological Dynamics (2011) 10.1080/17513758.2011.568071 |
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| Passing to the limit 2D-1D in a model for metastatic growth |
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| Sebastien Benzekry 1, 2 |
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| (2011-05-03) |
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| We prove the convergence of a family of solutions to a two-dimensional transport equation with a nonlocal boundary condition modeling the evolution of a population of metastases. We show that when the data of the repartition along the boundary tends to a dirac mass then the solution of the associated problem converges and we derive a simple expression for the limit in term of the solution of a 1D equation. This result permits to improve the computational time needed to simulate the model. |
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| 1: | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| 2: | Relations Hôtes Parasites Pharmacologie et Thérapeutique (UMR MD3) |
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Institut de Recherche Biomédicale des Armées – Université de la Méditerranée - Aix-Marseille II |
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| Subject | : | Mathematics/Analysis of PDEs |
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| Structured population dynamics – Cancer modeling – Angiogenesis |
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| hal-00521968, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00521968 | |
| oai:hal.archives-ouvertes.fr:hal-00521968 | |
| From: Sebastien Benzekry | |
| Submitted on: Wednesday, 29 September 2010 10:58:55 | |
| Updated on: Thursday, 17 January 2013 18:32:21 | |
