New results on group classification of nonlinear diffusion-convection equations

2003/06/30 by Roman O. Popovych, Nataliya M. Ivanova
Physics and Astronomy · Mathematics · #math-ph #math.AP #math.MP #nlin.SI #msc:35K57 #msc:35C05 #msc:58J70

paper · pdf · doi:10.1088/0305-4470/37/30/011

published as J. Phys. A: Math. Gen., 2004, V.37, N 30, 7547-7565 · LaTeX2e, 19 pages

arxiv created 2004/02/24 · arxiv updated 2009/11/30

Abstract

Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient (1+1)-dimensional nonlinear diffusion-convection equations of the general form f(x)u_t=(D(u)u_x)_x+K(u)u_x. We obtain new interesting cases of such equations with the density f localized in space, which have large invariance algebra. Exact solutions of these equations are constructed. We also consider the problem of investigation of the possible local trasformations for an arbitrary pair of equations from the class under consideration, i.e. of describing all the possible partial equivalence transformations in this class.

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