Penetrate The Cavity A Class Of Complex Positive Scattering Problem Vitro Obstacles

In this thesis,by using a point source as an electromagnetic wave,which is placed in a cavity.Let us discuss the question of scattering by the penetrable cavity and an outside unpenetrable obstacle.In the first chapter,let us consider the background and meaning,and as well as the arrangement of this thesis.In this thesis,let us consider the second chapter,it discuss the equation of scattering problem by the penetrable cavity and an unpenetrable barrier.Seeing the across section we find,we denote by(?)the complement of 1D and2 D,Assume that the penetrable cavity is denoted by 1D with smooth boundary 1?D,the unpenetrable obstacle is denoted by 2D with smooth boundary2?D,such that(?)One surface of the cavity is coated by some material with impedance 1? and ?,and the other surface of the barrier is coated by a material with impedance 2?,Let the point source iu locate in the cavity,the scattered fieldsu is formed in 1D,a transmitted wave v is formed in 2D.The impedance transmission boundary conditions are posed on the boundary ?D,the mixed type of Dirichlet-impedance conditions are posed on 2?D.Then,the wave fields satisfy the following Helmholtz equation with some condition :(?)(1)and v satisfies the Sommerfeld Radiation condition(?)are respectively on behalf of wave number in1 D and D,which are both positive constants.The incident waveiu and scatterd fieldsu are consist of the total field,(?)is the fundamental solution which is given by()(?)In this thesis,let us consider the third chapter,it use the boundary integral equation method to research the problem of scattering by a penetrate cavity and an outside crack.This thesis is mainly to prove the uniqueness of the above two direct scattering problems.At first,let us use Rellich lemma to discuss the uniqueness of the equation.Secondly,by using potential theory,the jump relation of single-layer and double-layer potentials,let us try to establish a boundary integral system,(A +B)U =R,where the operator A is invertible and B is compace,Finally by employing the Freholm theorem the uniqueness of the solution is obtained.