This article establishes the existence of trapped-mode solutions of a linearized water-wave problem. The fluid occupies a symmetric horizontal channel that is uniform everywhere apart from a confined region which either contains a thin vertical plate spanning the depth of the channel or has indentations in the channel walls. A trapped mode corresponds to an eigenvalue of a non-local Neumann-Dirichlet operator for an elliptic boundary-value problem in the fluid domain. The existence of such an eigenvalue is established by generalizing previous results concerning spectral theory for differential operators to this nan-local operator. (C) 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. [References: 12]
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机译：本文建立了线性化水波问题的陷波解的存在性。流体占据一个对称的水平通道，该水平通道除了封闭区域外，各处均是均匀的，该封闭区域要么包含横跨通道深度的薄垂直板，要么在通道壁上具有凹痕。对于流体域中的椭圆边界值问题，陷波模式对应于非局部Neumann-Dirichlet算子的特征值。通过将关于微分算子的频谱理论的先前结果推广到该南局部算子，可以建立这样一个特征值的存在。 （C）1997年，作者是B. G. Teubner斯图加特-约翰·威利父子有限公司[参考文献：12]
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