论文标题
Herglotz波函数，Vekua变换和外壳方法
The Herglotz wave function, the Vekua transform and the enclosure method
论文作者
论文摘要
本文提供了作者在二维中引入的典型逆障碍物和裂纹散射问题的应用程序的应用。未知多边形声音障碍物和分段线性裂纹的显式提取公式在固定波数上从散射场的远场图案中，并给出了最多两个入射方向。本文的主要新点是：围栏方法和HERGLOTZ波函数的组合；通过使用VEKUA变换的概念，明确构造了Herglotz波函数中的密度。借助构造，可以避免对提取公式中的波数进行任何限制。当还给出了以有限角度给出远场模式时的情况。
This paper gives applications of the enclosure method introduced by the author to typical inverse obstacle and crack scattering problems in two dimensions. Explicit extraction formulae of the convex hull of unknown polygonal sound-hard obstacles and piecewise linear cracks from the far field pattern of the scattered field at a fixed wave number and at most two incident directions are given. The main new points of this paper are: a combination of the enclosure method and the Herglotz wave function; explicit construction of the density in the Herglotz wave function by using the idea of the Vekua transform. By virtue of the construction, one can avoid any restriction on the wave number in the extraction formulae. An attempt for the case when the far field pattern is given on limited angles is also given.
