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Nonlinear Analysis: Real World Applications 9, 5 (2008) 2086-2105
A reaction–diffusion system modeling predator–prey with prey-taxis
Ahmed Noussair1, 2, Bedr'eddine Ainseba1, 2, Mostafa Bendahmane3

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.
1 :  IMB - Institut de Mathématiques de Bordeaux
2 :  INRIA Bordeaux - Sud-Ouest - ANUBIS
3 :  CI²MA - Centro de Investigación en Ingeniería Matemática [Concepción]
Reaction–diffusion system – Predator–prey – Prey-taxis – Finite volume scheme