Lipschitz stability in inverse problems for a Kirchhoff plate equation

Article type: Research Article

Authors: Yuan, Ganghua^; | Yamamoto, Masahiro

Affiliations: Department of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153, Japan E-mails: {ghyuan,myama}@ms.u-tokyo.ac.jp | Department of Mathematics, Northeast Normal University, Changchun, 130024, P.R. China

Abstract: In this paper, we are concerned with inverse problems of determining spatially varying two Lamé coefficients and the mass density by a finite number of boundary observations. Our main results are Lipschitz stability estimates for the inverse problems under suitable conditions on initial values and boundary values. In particular, if we take suitable quadratic functions as initial displacements, then we can prove the Lipschitz stability with the minimum times of observations.

Keywords: Kirchhoff plate, Carleman estimate, boundary observations, Lipschitz stability

Journal: Asymptotic Analysis, vol. 53, no. 1-2, pp. 29-60, 2007