Exact solutions of boundary-value problems for nonlinear flow in porous media (Q1082971)

Exact solutions for flow problems in porous media with a limiting gradient in the case when the flow region in the hodograph plane is a half-strip with a longitudinal cut are known only for two models of the resistance law. The present study gives a one-parameter family of flow laws, and argues the possibility of effective determination of exact and approximate analytical solutions on the basis of successive reduction to boundary-value problems for the Laplace equation or for the equation studied in detail by \textit{M. G. Bernadiner} and \textit{V. M. Entov}, The hydrodynamic theory of flow of anomalous fluids in porous media, Nauka, Moscow (1975). It should be noted that the characteristics of the flow are determined without additional quadratures.