Optimization method for the inverse coefficient problem of a parabolic equation

This paper studies an inverse coefficient problem of a parabolic equation where the final observation is given, the unknown coefficient depends on both the space variable x and the time variable t. Based on the optimal control framework, the inverse problem is transformed into an optimization problem and a new cost functional is constructed in the paper. The existence of the minimizer of the cost functional is proved, and the necessary conditions which must be satisfied by the minimizer are also given. (C) 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [CEIS 2011]