Abstract

We consider an initial–boundary value problem for a system of third-order partial differential equations in a rectangular domain. By introducing a new unknown function, we reduce the problem to an equivalent one consisting of a nonlocal problem for a system of second-order hyperbolic equations with parameters and integral relations. An iterative algorithm is proposed for approximately solving the equivalent problem, and its convergence is proved. Sufficient conditions in terms of the input data are established for the existence of a unique classical solution of the original problem.

中文翻译：

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三阶偏微分方程组初-边值问题的唯一可解性

摘要

我们考虑矩形域中三阶偏微分方程组的初边值问题。通过引入一个新的未知函数，我们将该问题简化为一个等效的问题，该问题由具有参数和积分关系的二阶双曲方程组的非局部问题组成。提出了一种迭代算法来近似求解等效问题，并证明了其收敛性。就输入数据而言，为原始问题的独特经典解的存在建立了充分条件。