Abstract

In this paper, we investigate a problem on small motions of a system of bodies partially filled with ideal fluids under the action of an elastic damping device. The initial boundary value problem is reduced to the Cauchy problem for a first-order differential operator equation on a Hilbert space. Properties of the resulting operator matrices, which are coefficients of the equation, are studied. Theorems on solvability of the Cauchy problem and the initial boundary value problem are proven.

中文翻译：

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弹性阻尼装置作用下充满理想流体的系统的小运动问题

摘要

在本文中，我们研究了在弹性阻尼装置的作用下部分充满理想流体的物体系统的小运动问题。对于希尔伯特空间上的一阶微分算子方程，初始边值问题简化为柯西问题。研究所得算子矩阵的性质，即方程的系数。证明了柯西问题和初边值问题的可解性定理。