Enhanced preliminary group classification of a class of generalized diffusion equations

Details Enhanced preliminary group classification of a class of generalized diffusion equations Enhanced preliminary group classification of a class of generalized diffusion equations

2010-12-01

arxiv.org/abs/1012.0297v2

Commun. Nonlinear Sci. Numer. Simulat. 16 (2011), 3622-3638

Physics

Mathematical Physics

22 pages, minor corrections

Scientific paper

10.1016/j.cnsns.2011.01.011

The method of preliminary group classification is rigorously defined, enhanced and related to the theory of group classification of differential equations. Typical weaknesses in papers on this method are discussed and strategies to overcome them are presented. The preliminary group classification of the class of generalized diffusion equations of the form u_t=f(x,u)u_x^2+g(x,u)u_{xx} is carried out. This includes a justification for applying this method to the given class, the simultaneous computation of the equivalence algebra and equivalence group, as well as the classification of inequivalent appropriate subalgebras of the whole infinite-dimensional equivalence algebra. The extensions of the kernel algebra, which are induced by such subalgebras, are exhaustively described. These results improve those recently published in Commun. Nonlinear Sci. Numer. Simul.

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