Lipschitz stability in the determination of the principal part of a parabolic equation
Department of Mathematical Sciences, The University of Tokyo,
Komaba Meguro, Tokyo, 153-8914, Japan. email@example.com; firstname.lastname@example.org
2 School of Mathematics & Statistics, Northeast Normal University, Changchun, Jilin, 130024, P. R. China.
Revised: 31 December 2007
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 aij 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.
Mathematics Subject Classification: 35R30 / 35K20
Key words: Inverse parabolic problem / Carleman estimate / Lipschitz stability
© EDP Sciences, SMAI, 2008