Propagación asintótica de la ecuación de reacción-difusión con condiciones Fisher-KPP

Abstract

In this paper we will study the existence, uniquenes and behavior of the solutions over large time of the one dimensional Cauchy problem for the reaction diffusion equation with Fisher-KPP non linearities on the reaction term and with a uniformly continuous and front-like initial conditions that decays more slowly than any other exponential function as x ->+oo. To study the existence and uniqueness we will use the Duhamel's principle and Banach's fixed point theorem. On the other hand, to study the asymptotic behavior of the solutions for the problem, we will use level sets, comparison principle, sub and super solutions (mild).