On a non-linear moving boundary problem for a diffusion–convection equation

Abstract

We study a one-dimensional free boundary problem for a non-linear diffusion convection equation whose diffusivity is heterogeneous in space as well as being non-linear. Under the B¨acklund transformation the problem is reduced to an associated free boundary problem. We prove the existence and uniqueness,local in time, of the solution by using the Friedman Rubinstein integral representation method and the Banach contraction theorem.