Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation

Abstract

In this paper substantiated for a differential equation of pseudoparabolic type with discontinuous coefficients a final-boundary problem with non-classical boundary conditions is considered, which requires no matching conditions. The considered equation as a pseudoparabolic equation generalizes not only classic equations of mathematical physics (heat-conductivity equations, string vibration equation) and also many models differential equations (telegraph equation, Aller's equation , moisture transfer generalized equation, Manjeron equation, Boussinesq-Love equation and etc.). It is grounded that the final-boundary conditions in the classic and non-classic treatment are equivalent to each other, and such boundary conditions are demonstrated in geometric form. Even from geometric interpretation can see that the grounded non-classic treatment doesn't require any additional conditions of agreement type. Thus, namely in this paper, the non-classic problem with final-boundary conditions is grounded for a pseudoparabolic equation of sixth order. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev anisotropic space WP(4,2)(G) .