可穿透腔体外有障碍物的正散射问题

Direct Scattering Problem for A Penetrable Cavity and An External Obstacle

分析了用点源作为入射波,散射体由一个可穿透腔体和一个外部不可穿透的障碍物组成的正散射问题,指出了该问题可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性和唯一性.

By using a point source as the incident wave ,we consider the scattering problem by a mixed scatterer which is composed of a penetrable cavity and an external impenetrable obstacle , and regard that this problem comes down to solving the Helmholtz equation with certain boundary conditions .By using the boundary integral equation method and based on the Fredholm theorem ,we prove that the scattering problem has a unique solution in the form of combined potentials .