Stability of backward-in-time semilinear coupled parabolic systems

TL;DR

This paper establishes conditional stability estimates for backward-in-time semilinear coupled parabolic systems in bounded domains, using a modified Carleman estimate approach with exponential weight functions.

Contribution

It introduces a new stability analysis method for strongly coupled semilinear parabolic systems employing a modified Carleman estimate with exponential weights.

Findings

Proved stability estimates for linear coupled parabolic systems.

Extended stability results to semilinear coupled systems.

Utilized a novel Carleman estimate technique with exponential weight.

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 $\lambda$.