A boundary value problem for a third-order equation with a nonlocal condition for the time

Abstract

At the end of the rectangular area in the unique solvability of a nonlocal boundary value problem for a third - order equation with multiple characteristics with the terms of the frequency with respect to time. Uniqueness of the solution of the problem is proved by the method of a priori estimates. The method of separation of variables for the particular case of the problem solution is constructed in the form of a Fourier series in eigenfunctions of the problem. Studied uniform convergence of the solution and its derivatives of order, included in the equation.