We consider a boundary value problem for a system of the fourth order pseudo-hyperbolic equations with nonlocal condition on a rectangular domain. By introducing a new unknown function, the considered problem is reduced to an equivalent nonlocal problem with integral condition for a system of hyperbolic integro-differential equations of the second order. We propose an algorithm for finding an approximate solution to the equivalent problem, and its convergence is proved basing on the functional parametrization method. Sufficient conditions of the unique existence of the classical solution to the boundary value problem for the system of the fourth order pseudo-hyperbolic equations with nonlocal condition are established in the terms of initial data.

我们考虑在矩形域上具有非局部条件的四阶伪双曲方程组的边值问题。通过引入一个新的未知函数，对于二阶双曲积分微分方程组，考虑的问题可以简化为带积分条件的等效非局部问题。我们提出了一种寻找等效问题近似解的算法，并基于函数参数化方法证明了其收敛性。根据初始数据，建立了具有非局部条件的四阶拟双曲方程组边值问题经典解的唯一解的唯一存在的充分条件。