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| Detailed view | Article in peer-reviewed journal |
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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 Noussair1, 2Bedr'eddine Ainseba1, 2Mostafa Bendahmane3 |
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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: | IMB - Institut de Mathématiques de Bordeaux |
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| 2: | INRIA Bordeaux - Sud-Ouest - ANUBIS |
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| 3: | CI²MA - Centro de Investigación en Ingeniería Matemática [Concepción] |
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| Reaction–diffusion system – Predator–prey – Prey-taxis – Finite volume scheme |
| hal-00391778, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00391778 | |
| oai:hal.archives-ouvertes.fr:hal-00391778 | |
| From: Ahmed Noussair | |
| Submitted on: Thursday, 4 June 2009 16:37:58 | |
| Updated on: Friday, 5 June 2009 09:39:59 | |