论文标题
弱奇异的任意顺序始终散布的分段分析界面
Piecewise-analytic interfaces with weakly singular points of arbitrary order always scatter
论文作者
论文摘要
事实证明，边界中包含一个弱奇异的任意秩序点的不均匀介质散布着每个传入波。同样，边界上具有弱奇异点的紧凑型源项总是辐射声波。这些结果意味着在不是$ c^\ indy $ smooth的域中没有非散射能量和非辐射来源。对于逆源和反向介质散射问题，获得了具有单个远场图案的局部唯一性结果。我们的论点提供了表面的足够条件，在该表面上，对Helmholtz方程的解决方案无法接受分析延续。
It is proved that an inhomogeneous medium whose boundary contains a weakly singular point of arbitrary order scatters every incoming wave. Similarly, a compactly supported source term with weakly singular points on the boundary always radiates acoustic waves. These results imply the absence of non-scattering energies and non-radiating sources in a domain that is not $C^\infty$-smooth. Local uniqueness results with a single far-field pattern are obtained for inverse source and inverse medium scattering problems. Our arguments provide a sufficient condition of the surface under which solutions to the Helmholtz equation admits no analytical continuation.
