Even and odd self-similar solutions of the diffusion equation for infinite horizon

Abstract

In the description of transport phenomena an important aspect represents the diffusion. In certain cases the diffusion may appear together with convection. In this paper we study the diffusion equation with the self similar Ansatz. With an appropriate change of variables we found original solutions of diffusion equation for infinite horizon. Here we present the even solutions of diffusion equation for the boundary conditions presented. For completeness the odd solutions are also mentioned as well, as part of the previous works. Finally, the diffusion equation with constant source term is discussed, which also has even and odd solutions, too