Аннотация
Abstract This article is devoted to the study of the solvability to a semiperiodic boundary value problem for an evolutionary equation of pseudohyperbolic type. Such problems were investigated in the works of many authors. This problem is reduced to a boundary value problem for a system of two pseudoparabolic equations of third order by a special replacement. To solve this problem we are introduced a new functions and applied the parameterization method. Then, the boundary value problem for system of the pseudoparabolic equations of third order is reduced to a family periodic boundary value problems for a system of ordinary differential equations. An algorithm for finding an approximate solution is proposed and conditions for the unique solvability of the problem under study are obtained.