Stability of backward-in-time semilinear coupled parabolic systems

Abstract

We consider backward problems for semilinear coupled parabolic systems in bounded domains. We prove conditional stability estimates for linear and semilinear systems of strongly coupled parabolic equations involving general semilinearities. The proof of the stability estimates relies on a modified method by Carleman estimates incorporating the simple weight function $e^{\lambda t}$ with a sufficiently large parameter $\lambda$.