Parabolic Systems with Nonlinear Competitive Interactions

摘要

A parabolic system with nonlinear local or nonlocal interactions is considered, with specific applications to the description of competition/combat situations. Global existence and comparison results are proven under suitable assumptions on the interaction terms. Comparisons with solutions of the ''equivalent'' ordinary differential (space independent) model, that has been previously used in modelling combat are of special interest. The stationary state of such a system--corresponding to a stalemate--is also considered. Under certain conditions on the interaction, domain size and boundary conditions, a uniqueness result is obtained for the stationary state. A simple example shows that these conditions are sharp and uniqueness may be lost when they are not fulfilled. 15 refs. (ERA citation 14:019140)