Exact solutions to nonlinear diffusion equations obtained by a generalized conditional symmetry method

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Abstract
In this paper, we discuss the reduction to Fujita's equation for the nonlinear diffusion equation under certain types of generalized conditional symmetry. It is shown that the nonlinear diffusion equation can be reduced to Fujita's equation if it admits a class of generalized conditional symmetry. As the results, some new exact solutions for a number of important nonlinear diffusion equations are obtained. Many of the solutions obtained here are illustrated graphically with particular reference to the phenomena of extinction, periodic property, blow-up and asymptotical behaviour.