This article presents an inverse source problem for a cascade system of $ n $ 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 $ n $ components at a fixed positive time $ T' $ over the whole spatial domain. The proof is based on the application of a Carleman estimate with a single observation acting on a subdomain.

中文翻译：

---

具有一个分量的局部分布观测的某些耦合退化退化抛物系统的Lipschitz稳定性

本文提出了耦合退化简并抛物方程的级联系统的反源问题。特别是，我们证明了反问题的稳定性和唯一性结果，该反问题是通过在任意一个子域中通过观察在一个固定的正时$ T'$上仅一个分量的时间间隔和$ n $分量的数据来确定源项的反问题的结果。整个空间领域。该证明是基于对单个子域进行单个观测的Carleman估计的应用。