Abstract
This paper is concerned with an inverse problem for the conduction of heat in a two-dimensional domain. It seeks to recover the subsurface conductivity profile based on the measurements obtained at the boundary. The method considers a temporal interval for which time-dependent measurements are provided. It formulates an optimal estimation problem which seeks to minimize the error difference between the given data and the response from the system. It uses a combination of the zeroth-order and the first-order Tikhonov regularization to stabilize the inversion. The method leads to an iterative algorithm which, at every iteration, requires the solution to a two-point boundary value problem. A number of numerical results are presented which indicate that a close estimate of the thermal conductivity function can be obtained based on the boundary measurements only. [S0022-1481(00)00902-6]
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