科研之友
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摘要
The scattering by a bounded or periodic rough surface is often modeled by assuming the plane wave incidence. However, when the rough surface is unbounded and nonperiodic, a tapered incident wave may be more appropriate to realize asymptotic truncation for the unbounded rough surface. Despite this extensive practical interest, little mathematical analysis of these problems has been carried out. This paper is concerned with the scattering and inverse scattering problem of the infinite impedance rough surfaces with tapered wave incidence. A boundary integral equation formulation is derived by using a half-plane impedance Green's function. It is shown that the integral equation is uniquely solvable in the space of bounded and continuous functions. Further, the impedance boundary value problem for the scattered field is proved to have a unique solution under certain constraints on the boundary impedance. It is also proved that a class of rough surfaces can be uniquely determined by the measurements of the scattered field generated by the tapered incident waves.
