Guozheng Yan

Inverse obstacle scattering with two scatterers

In this paper, we discuss the inverse scattering of two obstacles D11 and D12 with D11 C D11. For the sound-soft problem, we establish the uniqueness of the interior obstacle D11

The uniqueness of the inverse obstacle scattering problem with transmission boundary conditions

Abstract In this paper, we consider the uniqueness of the interior wavenumber for the inverse obstacle scattering problem with transmission boundary conditions. We show that the interior wavenumber is uniquely determined by the far field pattern.

The far field operator for a multilayered scatterer

In this paper, we consider the inverse problem of the scattering of a plane acoustic wave by a multilayered scatterer; especially we study the properties of the corresponding far field operator. This problem models time-harmonic acoustic or electromagnetic scattering by a penetrable homogeneous medium with an impenetrable core. The discussion is essential for numerical approximation of the corresponding inverse problem, i.e., from the knowledge of the far field patterns to model the shape of the scatterer

Uniqueness of the inverse conductive scattering problem

Abstract In this paper, we show that for the inverse obstacle scattering problem with conductive boundary condition, the conductive boundary is uniquely determined by the far field pattern.

Mathematical basis of scattering problems from penetrable obstacles and cracks

We consider a kind of scattering problem which models the scattering of an electromagnetic time-harmonic plane wave by an infinite cylinder having an open arc and a penetrable obstacle in R2 as cross section. To this end, we solve a scattering problem for the Helmholtz equation in R2 where the scattering object is a combination of a crack Γ and a penetrable obstacle D, and we have Dirichlet-Impedance type boundary condition on Γ and transmission boundary condition on ∂D. Applying potential theory, the problem can be reformulated as a boundary integral system. We establish the existence and uniqueness of a weak solution to the system by using the modified Fredholm theory.

Inverse scattering for transmission problem

Abstract This paper discusses the inverse obstacle scattering problem with transmission boundary condition. In particular, we shall show that transmission boundary is uniquely determined by the far field pattern.

Uniqueness of inverse scattering problem for a penetrable obstacle with rigid core

In this paper, we discuss the inverse scattering problem for a penetrable obstacle with an impenetrable rigid core. Using a generalization of Schiffers method to nonsmooth domains due to Ramm, we prove that the rigid core is uniquely determined by the far field patterns for a range of interior wavenumbers.

The boundary integral method for the Helmholtz equation with cracks inside a bounded domain

Abstract We consider a kind of scattering problem by a crack Γ that is buried in a bounded domain D , and we put a point source inside the domain D . This leads to a mixed boundary value problem to the Helmholtz equation in the domain D with a crack Γ. Both sides of the crack Γ are given Dirichlet-impedance boundary conditions, and different boundary condition (Dirichlet, Neumann or Impedance boundary condition) is set on the boundary of D . Applying potential theory, the problem can be reformulated as a system of boundary integral equations. We establish the existence and uniqueness of the solution to the system by using the Fredholm theory.

The direct and inverse problem for an inclusion within a heat-conducting layered medium

This paper is concerned with the problem of heat conduction from an inclusion in a heat transfer layered medium. Making use of the boundary integral equation method, the well-posedness of the forward problem is established by the Fredholm theory. Then an inverse boundary value problem, i.e. identifying the inclusion from the measurements of the temperature and heat flux on the accessible exterior boundary of the medium is considered in the framework of the linear sampling method. Based on a careful analysis of the Dirichlet-to-Neumann map, the mathematical fundamentals of the linear sampling method for reconstructing the inclusion are proved rigorously.

The direct scattering problem for a crack buried in a piecewise homogenous medium

We consider a kind of scattering problem which models the scattering of an electromagnetic time-harmonic plane wave by an infinite cylinder having an open arc and a penetrable obstacle in R2 as cross section, and the open arc is buried in a piecewise homogeneous medium. To this end, we solve a scattering problem for the Helmholtz equation in R2 where the scattering object is a crack Γ which is buried inside the bounded domain D, and we have Dirichlet-Impedance type boundary condition on Γ and transmission boundary condition on the boundary of D. Applying potential theory, the problem can be reformulated as a boundary integral system. We establish the existence and uniqueness of a weak solution to the system by using the modified Fredholm theory.