Gas pressure equalization in a porous medium filling a pipe with a closed end under shock loading

The problem of gas pressure equalization in a porous medium filling a pipe with a closed end under shock loading is solved. In this case, the initial filtration velocity behind the shock wave should be specified as initial data, in addition to the shock pressure. It is shown that the shock decays at a finite distance and pressure equalization occurs in a finite time. Approximate submodels of discontinuous and smooth solutions are obtained.