Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 9, Issue 5, Pages 2086-2105Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2007.06.017
Keywords
reaction-diffusion system; predator-prey; prey-taxis; finite volume scheme
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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. (c) 2007 Elsevier Ltd. All rights reserved.
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