Abstract
This paper discusses a class of (n+1)-dimensional nonlinear diffusion equations with source term which arises in nonlinear shear flows of non-Newtonian fluids. It is shown that some radially symmetric equations admit certain types of conditional Lie Bäcklund symmetries. As a result, exact solutions to the resulting equations are obtained. Those solutions extend the known ones such as instantaneous source solutions of the porous medium equation with absorption term. The phenomena of extinction and blow up and behavior to many of the solutions are described.
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