We consider stability and approximate reconstruction of Riemannian manifold when the finite number of eigenvalues of the LaplaceBeltrami operator and the boundary values of the corresponding eigenfunctions are given. The reconstruction can be done in stable way when manifold is a priori known to satisfy natural geometrical conditions related to curvature and other invariant quantities.

In this paper, a boundary integral method is used to solve an inverse heat conduction problem. An algorithm for the inverse problem of the one dimensional case is given by using the fundamental solution. Numerical results show that our algorithm is effective.

The continuous casting process of metals and alloys is nowadays frequently utilized in metallurgical industry, and more general in material engineering. Typically, the liquid material flows into the mould (crystallizer) having the walls cooled by flowing water. The solidifying ingot is pulled out by the withdrawal rolls. Below the mould the side surface of the ingot is very intensively cooled b...

Let DcR' be a bounded domain with a smooth boundary r, A u + q ( x ) u = O in D u = f , u N = h on Iand ~ ( x ) E L ~ ( D ) . From knowledge of the set {f, h} where f runs through C'(r) the coefficient 9(x) is uniquely recovered. Analytical formulae for y(x) are given. Applications are considered. Let D c R3 be a bounded domain with a smooth boundary r, q(x) E L"(D) , A u + q ( x ) u = O in D U...

We show how to eliminate the error caused by an incorrectly modeled boundary in electrical impedance tomography (EIT). In practical measurements, one usually lacks the exact knowledge of the boundary. Because of this the numerical reconstruction from the measured EIT–data is done using a model domain that represents the best guess for the true domain. However, it has been noticed that the inacc...

In this paper, we prove that the inverse problems for 2D elasticity and for the thin plate with boundary data (finite or full measurements) are equivalent. Having proved this equivalence, we can solve inverse problems for the plate equation with boundary data by solving the corresponding inverse problems for 2D elasticity, and vice versa. For example, we can derive bounds on the volume fraction...

This paper presents a limited survey of methods and multidisciplinary applications of various techniques for the solution of several classes of inverse problems as developed and practiced by our research team. Sketches of solution methods for inverse problems of shape determination, boundary conditions determination, sources determination, and physical properties determination are presented fro...

We show that in dimension two or greater, a certain equivalence class of the scalar coefficient a(x, u) of the semilinear elliptic equation ∆u + a(x, u) = 0 is uniquely determined by the Dirichlet to Neumann map of the equation on a bounded domain with smooth boundary. We also show that the coefficient a(x, u) can be determined by the Dirichlet to Neumann map under some additional hypotheses.