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IMA Journal of Applied Mathematics 1999 62(3):283-302; doi:10.1093/imamat/62.3.283
© 1999 by Institute of Mathematics and its Applications
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Exact solutions to nonlinear diffusion equations obtained by a generalized conditional symmetry method

Q Changzheng

Department of Mathematics, Northwest University, Xi'an 710069, PRC Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, ROC

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.


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