On the identification of coefficients of elliptic problems by asymptotic regularization

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Abstract
The problem of recovering coefficients of elliptic problems from measured data is considered. An algorithm is developed to identify the unknown coefficients without a minimization technique. The method is based on the construction of certain time-dependent problems which contain the original equation as asymptotic steady state. A Liapunovtype a-priori estimate is fundamental to prove that the solution of the time-dependent regularized equations approach a solution of the original problem as t →∞. A related behavior is proved for the solution of corresponding finite-dimensional Galerkin approximations. A stability result is proved for the Galerkin approximations.

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