Abstract

In this paper, we consider the questions of the unique solvability of a boundary value problem for a third-order partial integro-differential equation with a degenerate kernel and multiple characteristics. An explicit solution of the boundary value problem is constructed. In this case, a combination of three methods was used: the method for constructing Green’s function, the method of Fourier series and the Fredholm method for the degenerate kernel.

中文翻译：

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具有退化核的三阶偏积分微分方程的边值问题

摘要

在本文中，我们考虑了具有退化核和多特征的三阶偏积分微分方程边值问题的唯一可解性问题。构造了边值问题的显式解。在这种情况下，使用了三种方法的组合：构造格林函数的方法、傅立叶级数的方法和退化核的 Fredholm 方法。