无限边界上的表面波

IF 0.7 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2025-10-17 DOI:10.1134/S1234567825030115

Dmitrii Yafaev

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引用次数: 0

摘要

建立了半空间中具有Robin型边界条件的拉普拉斯算子的散射理论。特别是，我们表明，除了通常的空间波存在于锥体中并由标准波算符描述之外，表面波也可能出现在这个问题中。它们定域在边界的抛物线邻域中。我们找到了表面波存在的边界系数条件。提出了几个悬而未决的问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Surface Waves on Infinite Boundaries

We develop scattering theory for the Laplace operator in the half-space with Robin type boundary conditions on the boundary plane. In particular, we show that, in addition to usual space waves living in cones and described by standard wave operators, surface waves may arise in this problem. They are localized in parabolic neighbourhoods of the boundary. We find conditions on the boundary coefficient ensuring the existence of surface waves. Several open problems are formulated.

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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.