Abstract
In this study the method of Kulish has been used to derive a non-field solution of the equation, which models the process of unsteady filtration of a slightly compressible fluid within a domain consisting of both flow and stagnation areas under the influence of some pressure distribution at the boundary. The solution relates the local values of pressure and the corresponding pressure gradient and is valid everywhere within the domain including the boundary. The solution thus obtained is in the form of a series with respect to generalised differ-integral operators of fractional orders. The solution has been compared with the know solution of the filtration problem with no stagnation areas. Finally, an integral equation to estimate the pressure evolution at the boundary for a given filtration speed has been proposed.
Asymptotics of inverse filtration problem in porous media
