On a Parabolic Variational Inequality That Generalizes the Equation of Polytropic Filtration

Abstract

We obtain conditions for the existence and uniqueness of a solution of a parabolic variational inequality that is a generalization of the equation of polytropic elastic filtration without initial conditions. The class of uniqueness of a solution of this problem consists of functions that increase not faster than e ^−μt , μ > 0, as t → −∞.