Nonlinear Parabolic Predator-Prey Coupled System With Convection

The aim of this work is to provide a formulation of two related nonlinear diffusive convective models in the form of coupled reaction-absorption equations. First, the postulated models are studied with an analytical approach. Later on, numerical evidences are considered to account for a precise characterization. The problem (P) analyzed is of the form:u(t) = delta Delta u + c . del u + v(n),u(t) epsilon Delta v + c . del v - u(m), m,m is an element of(0,1), (0,1)U-0 (x), v(0) (x) > 0 is an element of L-loc(1) (R-N) boolean AND L-infinity (R-N).Afterwards, a related problem P-T is studied:u(t) = delta Delta u + c . del u - v(n) (u - d),v(t) - epsilon Delta v + c . del v - u(m)v, n, m is an element of(0,1) (0,2)u(0) (x), v(0) (x) > 0 is an element of L-loc(1)(RN) boolean AND L-infinity (R-N).The principal aspects for analysis are related to the existence and the derivation of particular solutions to reproduce the dynamic of the interacting species. For the problem P-T, we make use of the TW approach to study existence of solutions and precise evolution of profiles.Note that the term predator is used to refer to an invasive behavior, while the term prey is used for the invaded species.