Abstract

We consider the second boundary-value problem for a third-order equation with multiple characteristics containing the second derivative with respect to time in a rectangular domain. Uniqueness of the solution is proved by the energy integral method. The Green’s function is constructed for the second boundary-value problem, through which an explicit solution of the problem is written.

中文翻译：

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粘性跨音速方程边值问题的唯一可解性

摘要

我们考虑了一个三阶方程的第二边值问题，该方程具有多个在矩形域中相对于时间包含第二阶导数的特征。通过能量积分法证明了该解的唯一性。格林函数是为第二个边值问题构造的，通过它写出问题的显式解。