Recovering a Lamé kernel in a viscoelastic equation by a single boundary measurement

Abstract

We consider the viscoelasticity equation and the problem of recovering the spatial part p(x) of the Lamé kernel depending on two spatial variables. We obtain a stability estimate of the solution to this problem.

Keywords:

• viscoelasticity equation
• inverse problem
• stability estimate

AMS Subject Classifications:

• primary 45Q05
• secondary 45K05

Acknowledgements

This article was written during the first author's stay in January–February of 2009 at the Graduate School of Mathematical Sciences of University of Tokyo, and the stay was supported by Global COE Program ‘The Research and Training Center for New Development in Mathematics’. He heartily thanks Professor Masahiro Yamamoto for the invitation and great efforts for making the stay very comfortable and fruitful. The author was partly supported by the Russian Foundation for Basic Research (grant No. 08-01-00312). The authors thank Professor Alfredo Lorenzi for careful reading of this article and valuable comments and remarks.