报告人： Prof.Jean-Claude Nedelec
The Helmholtz Equation in a Half-space with a Mixed Boundary Condition
We obtain existence and uniqueness results for the Helmholtz equation in the half-space $\rr^3_+$ with an impedance or Robin boundary condition. We compute the associated Green's function with the help of a double Fourier transform and we analyze its far field in order to obtain radiation conditions that allow to prove the uniqueness of an outgoing solution. These radiation conditions are somewhat unusual due to the appearance of a surface wave guided by the boundary. An integral representation of the solution is presented by mean of the Green's function and the boundary data. An extension to the case of a locally perturbed domain is then presented.
报告时间： 2006年7月21日(周五) 下午3:00--4:00