The Samarsky – Ionkin Problem with Integral Perturbation for a Pseudoparabolic Equation

Abstract

In the work the solvability of nonlocal boundary value problems for thirdorder pseudoparabolic equations in anisotropic spaces of Sobolev is studied. The condition is specified by a spatial variable that combines the generalized Samarsky-Ionkin condition and the integral type condition is particularity of the problems under study. The work aim is to prove the existence and uniqueness of the problems regular solutions - the solutions that have all Sobolev derivatives included in the corresponding equation.

Keywords

• sobolev type differential equations of the third order
• spatially-nonlocal boundary value problems
• generalized samarsky-ionkin condition
• regular solutions
• existence and uniqueness