可穿透腔体外有裂缝的正散射问题

The Direct Scattering Problem for a Penetrable Cavity and a Crack

研究了时间调和的点源入射平面波通过腔体和裂缝的正散射问题,认为散射体是由一个可穿透腔体和一个外部不可穿透的裂缝构成,该问题归结为对具有一定边界条件的Helmholtz方程的求解.通过边界积分方程的方法,利用位势理论和Fredholm定理,证明了该问题解的存在唯一性.

In this paper,by using a time harmonic point source as the incident wave,we consider the scattering problem of a mixed scatterer composed of a penetrable cavity and an external impenetrable crack. The problem comes down to solving the Helmholtz equation with certain boundary conditions. By using the boundary integral equation method,based on the potential theory and Fredholm theorem,we prove that the scattering problem has a unique solution.