First we establish a Carleman estimate with a single observation acting on a subdomain for the phase field system in a bounded domain [image omitted] 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 [image omitted].
Bibliographical noteFunding Information:
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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics