On a prey-predator reaction-diffusion system with Holling type III functional response

In this paper we study a prey-predator model defined by an initial-boundary value problem whose dynamics is described by a Holling type III functional response We establish global existence and uniqueness of the strong solution. We prove that lithe initial data are positive and satisfy a certain regularity condition, the solution of the problem is positive and bounded on the domain Q = (0, T) x Omega and then we deduce the continuous dependence on the initial data. A numerical approximation of the system is carried out with a spectral method coupled with the fourth-order Runge-Kutta time solver. The biological relevance of the comparative numerical results is also presented. (C) 2010 Elsevier B V All rights reserved