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| HAL : hal-00391778, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Nonlinear Analysis: Real World Applications 9, 5 (2008) 2086-2105 |
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| A reaction–diffusion system modeling predator–prey with prey-taxis |
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| Ahmed Noussair 1, 2Bedr'eddine Ainseba 1, 2 |
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| Conycit INRIA-Chili Collaboration(s) |
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| (04/12/2008) |
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| We are concerned with a system of nonlinear partial differential equations modeling the Lotka–Volterra interactions of predators and preys in the presence of prey-taxis and spatial diffusion. The spatial and temporal variations of the predator's velocity are determined by the prey gradient. We prove the existence of weak solutions by using Schauder fixed-point theorem and uniqueness via duality technique. The linearized stability around equilibrium is also studied. A finite volume scheme is build and numerical simulation show interesting phenomena of pattern formation. |
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| 1 : | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| 2 : | ANUBIS (INRIA Bordeaux - Sud-Ouest) |
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INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR |
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| 3 : | Centro de Investigación en Ingeniería Matemática [Concepción] (CI²MA) |
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Universidad de Concepción |
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| Domaine | : | Statistiques/Calcul Mathématiques/Equations aux dérivées partielles |
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| Reaction–diffusion system – Predator–prey – Prey-taxis – Finite volume scheme |
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| hal-00391778, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00391778 | |
| oai:hal.archives-ouvertes.fr:hal-00391778 | |
| Contributeur : Ahmed Noussair | |
| Soumis le : Jeudi 4 Juin 2009, 16:37:58 | |
| Dernière modification le : Vendredi 5 Juin 2009, 09:39:59 | |
