Ondas viajantes para um modelo de combustão em meios porosos e para a equação KPP.

Abstract

In this work is presented a study about the existence and uniqueness of traveling waves solutions for two classes of differential equations. The first of them is a system modeling a temperature front propagation in a porous media. This model come from a thermal method applied to oil recovery in petroleum engineering. For this model it is proved the existence and uniqueness of a traveling wave solution for a range of propagation velocities above a critical value. The existence is proved by the geometric singular perturbation technique and the uniqueness by the Melnikov Integral. The second class is a reaction-diffusion equation known in literature as the KPP equation. This equation come from isothermal autocatalytic chemical reactions problems. By analogous techniques used in the first class are obtained analogous results on the existence and uniqueness of traveling wave solutions. The workfinisheswiththespectralstabilitystudyofthetravelingwaveswithnoncritical velocities of the KPP equation under perturbations in a weighted Banach space.