Consider   the electromagnetic scattering and inverse scattering problems by rough   surfaces and obstacles. In this talk, we mainly focus on acoustic waves and   electromagnetic wave cases. The asymptotic behavior of Green’s tensor   function is analyzed and plays an important role in the analysis of the   well-posedness of the direct problem. By introducing an energy decaying   condition, a novel boundary integral equation is proposed for the   associated boundary value problem. Based on the related boundary integral equation   method, we prove the well-posedness of the composite scattering problem. For   the inverse problem, we intend to answer the following question: what   information can we extract about the obstacle and the unbounded rough surface   from the tangential trace of the electric field measured on the plane surface   which is above and below the obstacle and unbounded rough surface,   respectively? We show that any two obstacles and unbounded rough surfaces are   identical if they generate the same data.The proof is based on a combination of Holmgren's uniqueness and unique   continuation. The second result is concerned with local stability. A crucial step in the stability proof is to obtain the existence and characterization of the domain derivative of the electric field with respect to the shape of the obstacle and unbounded rough surface.

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会议密码：202006