Resumen de Stability of Diffusion Coefficients in an Inverse Problem for the Lotka-Volterra Competition System

K. Sakthivel, N. Baranibalan, J.-H. Kim, K. Balachandran

• 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.