In this paper, we consider an inverse problem of determining the corrosion occurring in an inaccessible interior part of a pipe from the measurements on the outer boundary. The problem is modelled by Laplace's equation with an unknown term γ in the boundary condition on the inner boundary. Based on the Maz'ya iterative algorithm, a regularized BEM method is proposed for obtaining approximate solutions for this inverse problem. The numerical results show that our method can be easily realized and is quite effective.
The inverse problem of determining two convection coefficients of an elliptic partial differential equation by Dirichlet to Neumann map is discussed.It is well known that this is a severely ill-posed problem with high nonlinearity.By the inverse scattering technique for first order elliptic system in the plane and the theory of generalized analytic functions,we give a constructive method for this inverse problem.
The authors prove the uniqueness in the inverse acoustic scattering problem within convex polygonal domains by a single incident direction in the sound-soft case and the sound-hard case, and by two incident directions in the case of the impedance boundary condition. The proof is based on analytic continuation on a straight line.
