Abstract:The two-dimensional (2D) domain under study is bounded from below by two semi-infinite and, between them, two finite straight lines; on each of the straight lines (segments), a usually individual impedance boundary condition is imposed. An incident surface wave, propagating from infinity along one semi-infinite segment of the polygonal domain, excites outgoing surface waves both on the same segment (a reflected wave) and on the second semi-infinite segment (a transmitted wave); in addition, a circular (cylindrical) outgoing wave will be generated in the far field. The scattered wave field satisfies the Helmholtz equation and the Robin (in other words, impedance) boundary conditions as well as some special integral form of the Sommerfeld radiation conditions. It is shown that a classical solution of the problem is unique. By the use of some known extension of the Sommerfeld–Malyuzhinets technique, the problem is reduced to functional Malyuzhinets equations and then to a system of integral equations of the second kind with integral operator depending on a characteristic parameter. The Fredholm property of the equations is established, which also leads to the existence of the solution for noncharacteristic values of the parameter. From the Sommerfeld integral representation of the solution, the far-field asymptotics is developed. Numerical results for the scattering diagram are also presented.

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中文翻译：

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具有阻抗边界的多边形域中的表面波散射

摘要：所研究的二维（2D）域从下方以两条半无限为界，在它们之间以两条有限直线为界；在每条直线（线段）上，通常会施加一个单独的阻抗边界条件。沿多边形域的一个半无限段从无穷远处传播的入射面波在同一段（反射波）和第二个半无限段（透射波）上激发出射面波；此外，在远场会产生一个圆形（圆柱形）出射波。散射波场满足亥姆霍兹方程和罗宾（即阻抗）边界条件以及索末菲辐射条件的一些特殊积分形式。表明该问题的经典解决方案是唯一的。通过使用 Sommerfeld-Malyuzhinets 技术的一些已知扩展，问题被简化为函数 Malyuzhinets 方程，然后是第二类积分方程组，其积分算子取决于特征参数。方程的Fredholm性质成立，这也导致了参数非特征值解的存在。从解的 Sommerfeld 积分表示，发展了远场渐近法。还给出了散射图的数值结果。方程的Fredholm性质成立，这也导致了参数非特征值解的存在。从解的 Sommerfeld 积分表示，发展了远场渐近法。还给出了散射图的数值结果。方程的Fredholm性质成立，这也导致了参数非特征值解的存在。从解的 Sommerfeld 积分表示，发展了远场渐近法。还给出了散射图的数值结果。

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