ABSTRACT

In this paper, we study inverse source problems for the heat equation with an inverse-square potential localized on the boundary of a smooth bounded domain, and with a locally distributed observation. We first derive an improved Carleman estimate of that obtained by Cazacu [SIAM J Control Optim. 2014;52:2055–2089] and then use it to prove the Lipschitz stability result for the inverse source problem.

中文翻译：

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奇异抛物方程逆源问题中的 Lipschitz 稳定性

摘要

在本文中，我们研究了热方程的逆源问题，该方程具有位于光滑有界域边界上的平方反比势，并且具有局部分布的观察结果。我们首先推导出 Cazacu [SIAM J Control Optim. 2014;52:2055–2089]，然后用它来证明逆源问题的 Lipschitz 稳定性结果。