Abstract

In this research work, for a third-order elliptic-hyperbolic type equation, a method for studying a nonlocal boundary-value problem by solving the inverse problem for a second-order mixed elliptic-hyperbolic type equation with an unknown right-hand side was proposed. A new extremume principle for a third-order equation was developed, and with the help of which the uniqueness of the problem is proved. Studying of the existence of solution of the investigated problem, by usingfunctional relations obtained a singular integral equation. Was determined the necessary class of given functions, which provide solvability of the obtained singular equation. Using the general presentation of solution, the solution of the investigated problem is completely constructed in the corresponding domains.

中文翻译：

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三阶椭圆-双曲型方程的非局部边值问题

摘要

在这项研究工作中，对于三阶椭圆-双曲型方程，通过求解右手未知的二阶混合椭圆-双曲型方程的反问题来研究非局部边值问题的方法建议。提出了一种新的三阶方程极值原理，并借助其证明了问题的唯一性。对所研究问题的解的存在性进行研究，利用函数关系式得到了奇异积分方程。确定了给定函数的必要类，这些函数提供了获得的奇异方程的可解性。使用解决方案的一般表示，可以在相应的域中完全构建要研究的问题的解决方案。