Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
838504 | Nonlinear Analysis: Real World Applications | 2008 | 20 Pages |
Abstract
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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Authors
Bedr’Eddine Ainseba, Mostafa Bendahmane, Ahmed Noussair,