Lipschitz stability for some coupled degenerate parabolic systems with locally distributed observations of one component

Abstract

This article presents an inverse source problem for a cascade system of \begin{document}$ n $\end{document} coupled degenerate parabolic equations. In particular, we prove stability and uniqueness results for the inverse problem of determining the source terms by observations in an arbitrary subdomain over a time interval of only one component and data of the \begin{document}$ n $\end{document} components at a fixed positive time \begin{document}$ T' $\end{document} over the whole spatial domain. The proof is based on the application of a Carleman estimate with a single observation acting on a subdomain.