On the identification of coefficients of elliptic problems by asymptotic regularization |
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Authors: | Prof Dr K -H Hoffmann Prof Dr Jürgen Sprekels |
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Institution: | Mathematisches Institut der Universitat Augsburg , Memminger Str. 6, Augsburg, D-8900, West-Germany |
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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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