Perturbaciones singulares sobre una clase de ecuaciones diferenciales

Abstract

In this paper we deal with a particular equation of a class of partial differential equations. We focus on the continuity of the solution which is given by the method of characteristic curves. More specifically, the generalized Burgers equation. This is a differential equation well known for mathematical analysis and for its applications. It is commonly used in traffic flow and fluid motion models. In finite time there is a singularity also called blow-up that generates discontinuities even if the initial conditions are continuous. We describe the continuous solution given by the singularity. And we employ the singular perturbation technique to find a correction to the position at the discontinuity.