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Conditional Lie-Bäcklund symmetries and reductions of the nonlinear diffusion equations with source. (English) Zbl 1468.35007

Summary: Conditional Lie-Bäcklund symmetry approach is used to study the invariant subspace of the nonlinear diffusion equations with source \(u_t = e^{- q x}(e^{p x} P(u) u_x^m)_x + Q(x, u)\), \(m \neq 1\). We obtain a complete list of canonical forms for such equations admit multidimensional invariant subspaces determined by higher order conditional Lie-Bäcklund symmetries. The resulting equations are either solved exactly or reduced to some finite-dimensional dynamic systems.

MSC:

35A30 Geometric theory, characteristics, transformations in context of PDEs
35K59 Quasilinear parabolic equations
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