Lipschitz stability in the determination of the principal part of a parabolic equation

¹ Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro, Tokyo, 153-8914, Japan. g_h_yuan@hotmail.com; myama@ms.u-tokyo.ac.jp
² School of Mathematics & Statistics, Northeast Normal University, Changchun, Jilin, 130024, P. R. China.

Received: 7 March 2007
Revised: 31 December 2007

Abstract

Let y(h)(t,x) be one solution to with a non-homogeneous term h, and , where is a bounded domain. We discuss an inverse problem of determining n(n+1)/2 unknown functions a_ij by , after selecting input sources suitably, where is an arbitrary subboundary, denotes the normal derivative, and . In the case of , we prove the Lipschitz stability in the inverse problem if we choose from a set with an arbitrarily fixed subdomain . Moreover we can take by making special choices for , . The proof is based on a Carleman estimate.