A free boundary problem for a diffusion-convection equation

Abstract

One-dimensional free boundary problem for a nonlinear diffusion - convection equation with a Dirichlet condition at fixed face $x=0$, variable in time, is considered. Throught several transformations the problem is reduced to a free boundary problem for a diffusion equation and the integral formulation is obtained. By using fixed point theorems, the existence of at least a solution, for small time, to a system of coupled nonlinear integral equations is obtained.