Solution of Some Free Boundary Problem of The Pseudo Parabolic Type With The Methods of The Variational Inequalities

Abstract

In the paper we consider some free boundary problem of the pseudo parabolic type. We prove the equivalence thisproblem with the corresponding problem of the variational inequalities (by sufficient smoothness of the solution ofthe variational inequality), as well as prove existence, uniqueness and smoothness theorems for the weak solution ofthe variational inequality under some assumptions.