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

Yung, C. M.; Verburg, K.; Baveye, P.

Int. J. Non-Linear Mech. 29, No. 3, 273-278 (1994).

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”.

Reviewer: P.Hillion (Le Vesinet)

MSC:

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

Keywords:

Painlevé conjecture; nonlinear diffusion-convection equation