Mathematical models of filtering in an extended loading layer

The study of liquid or gas motion in a porous medium in the framework of classical models does not always adequately describe the real processes. This is due to the fact that in these models the presence of a non-stationary source is not taken into account. The same applies to the models of a filtering in the extended loading layer. For a more adequate description of the real processes of the filtering in the extended loading layer in the presence of a non-stationary source, we took the invariant submodels of a well-tested, adequately reflecting real processes without a source, Leibenzon model, to which we added a non-stationary source, which is singular at the initial time. Such sources are often found in a practice. We studied the invariant submodels of this model, which are described by exact solutions. We found their physical meaning. For particular values of the parameters that determine these submodels, a pressure distribution grafs are constructed.