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On double reductions from symmetries and conservation laws. (English) Zbl 1179.35038

Summary: We present the theory of double reductions of PDEs with two independent variables that admit a Lie point symmetry and a conserved vector invariant under the symmetry. The theory is applied to a third order nonlinear partial differential equation which describes the filtration of a visco-elastic liquid with relaxation through a porous medium.

MSC:

35B06 Symmetries, invariants, etc. in context of PDEs
76S05 Flows in porous media; filtration; seepage
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