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Group classification and symmetry reductions of the nonlinear diffusion- convection equation \(u_ t=(D(u)u_ x)_ x-K'(u)u_ x\). (English) Zbl 0809.35042
Authors’ summary: “A nonlinear diffusion-convection equation arising from the theory of transport in porous media is analyzed using the Lie group technique. A complete classification of the functional forms of the transport coefficients is presented for which different symmetry groups are admitted. For a number of interesting cases, symmetry reductions are performed leading to exact group invariant solutions. In particular, the special case of the (integrable) Fokas-Yortsos equation is examined in the light of the “Painlevé conjecture” concerning the symmetry reductions of integrable PDEs”.

35K57 Reaction-diffusion equations
76S05 Flows in porous media; filtration; seepage
76R99 Diffusion and convection
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