First we establish a Carleman estimate for Lotka-Volterra competition-diffusion system of three equations with variable coefficients. Then the internal observations with two measurements are allowed to obtain the stability result for the inverse problem consisting of retrieving two smooth diffusion coefficients in the given parabolic system for the dimension n≤3. The proof of the results rely on Carleman estimates and certain energy estimates for parabolic system.
Bibliographical noteFunding Information:
The work of the first author was supported by the Brain Korea 21 project at Yonsei University, 2008. The third author research 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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics