We consider the initial boundary value problem for the heat equation in a region with in nite and nite boundaries (direct problem) and the related problem to reconstruct the nite boundary from Cauchy data on the in nite boundary (inverse problem). The numerical solution of the direct problem is realized by a boundary integral equation method. For an approximate solution of the inverse problem w...

Optical Aharonov-Bohm effect: an inverse hyperbolic problems approach. Abstract We describe the general setting for the optical Aharonov-Bohm effect based on the inverse problem of the identification of the coefficients of the governing hyperbolic equation by the boundary meas-rements. We interpret the inverse problem result as a possibility in principle to detect the optical Aharonov-Bohm effe...

In this paper, a boundary integral method is used to solve an inverse linear heat conduction problem in two-dimensional bounded domain. An inverse problem of measuring the heat flux from partial (on part of the boundary) dynamic boundary measurements is considered. An algorithm is given by using the fundamental solution.

The paper deals with the inverse determination of heat source in an unsteady heat conduction problem. The governing equation for the unsteady Fourier heat conduction in 2D region with unknown internal heat source is known as the inverse boundary-initial-value problem. The identification of strength of the heat source is achieved by using the boundary condition, initial condition and a known val...

We consider the inverse problem for identification of the coefficient in an elliptic partial differential equation inside of the unit square D, with overposed boundary data. This problem is not investigated enough in the literature due to lack of results about the uniqueness of the inverse problem. Following the main idea of the so-called Method of Variational Imbedding (MVI), we embed the solu...

The inverse potential problem consists in reconstructing an unknown measure with support in a geometrical domain from a single boundary measurement. In order to deal with this severely ill-posed inverse problem, we rewrite it as an optimization problem where a KohnVogelius-type functional measuring the misfit between the solutions of two auxiliary problems is minimized. One auxiliary problem co...

This paper examines uniqueness and stability results for an inverse problem in thermal imaging. The goal is to identify an unknown boundary of an object by applying a heat flux and measuring the induced temperature on the boundary of the sample. The problem is studied in both the case in which one has data at every point on the boundary of the region and the case in which only finitely many mea...