Stability estimate for an inverse wave equation and a multidimensional Borg–Levinson theorem

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• 作者：Mourad Bellassoued ; Mourad Choulli ; Masahiro Yamamoto
• 刊名：Journal of Differential Equations
• 出版年：2009
• 出版时间：15 July 2009
• 年：2009
• 卷：247
• 期：2
• 页码：465-494
• 全文大小：331 K

文摘

We consider the stability in an inverse problem of determining the potential q entering the wave equation in a bounded smooth domain of from boundary observations. The observation is given by a hyperbolic (dynamic) Dirichlet to Neumann map associated to a wave equation. We prove a log-type stability estimate in determining q from a partial Dirichlet to Neumann map provided that q is a priori known in a neighbourhood of the boundary of the spatial domain and satisfies an additional condition. Next, we use this result to establish a stability estimate related to the multidimensional Borg–Levinson theorem.