On the identification of coefficients of elliptic problems by asymptotic regularization

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.