On a Certain Semilinear Parabolic System Related to the Lotka-Volterra Ecological Model

Abstract

A mathematical model proposed to explain the horizontal structure of prey and predator populations is represented by a semilinear parabolic system of equations. In this paper some mixed problems for this kind of system, Lotka-Volterra system, are considered and asymptotic behaviors of the solutions are investigated by use of Energy Method. A remarkable fact is that, in opposition to Steele's conjecture (see [3]), the solution in the case of the Neumann boundary condition is asymptotically spatially homogeneous but does not tend to any constant steady state solution.