Abstract
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―Backlund 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.
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