Inverse problems for the phase field system with one observation

Abstract

First we establish a Carleman estimate with a single observation acting on a subdomain for the phase field system in a bounded domain Then this estimate is successfully used along with certain energy estimates to obtain the stability result for the inverse problem consisting of retrieving a smooth diffusion coefficient in the given system for the dimension

Keywords:

• inverse problems
• phase field model
• Carleman estimate

AMS Subject Classifications::

• 35K05
• 35R30
• 80A22

Acknowledgements

The work of K. Sakthivel was supported by the Brain Korea 21 project at Yonsei University, 2008. The work of J.-H. Kim was financially supported by the Ministry of Knowledge Economy (MKE) and Korea Industrial Technology Foundation (KOTEF) through the Human Resource Training Project for Strategic Technology, 2008.