Nonlinear problem of the filtration field of a flat flow

The nonlinear problem of the pressure field in the case of one-dimensional planar filtration is considered, when changes in the density of the skeleton, as well as the filtered fluid, and pressure are proportionally related. To solve the problems, an asymptotic method is used, based on the introduction of a formal parameter in the problem under consideration and the representation of the desired solution in the form of an asymptotic formula for this parameter. It is shown that the statements of the corresponding problems for the asymptotic expansion coefficients are linear, and classical methods can be used to solve them. Analytical expressions for the coefficients of asymptotic expansion of the solution have been found. It is shown that the corresponding expansion coefficients of the residual term of the current number and all the preceding ones in the same formal parameter as for the desired solution vanish. The approach used opens up new possibilities for solving nonlinear filtering problems in an inhomogeneous anisotropic porous medium.