Solutions and symmetry reductions of the n-dimensional non-linear convection–diffusion equations

摘要

This paper discusses a wide class of n-dimensional non-linear convection–diffusion equations with source term. It is shown that the radially symmetric equations admit certain types of conditional Lie–B¨acklund symmetries. As a result, exact solutions and symmetry reductions to 2D dynamical systems of the resulting equations are obtained. Those solutions extend the known ones such as self-similar solutions and instantaneous source-type solutions of the porous medium equation with absorption term. The behaviour of extinction and blow-up to many of the solutions are described.