Logarithmic stability in determination of a coefficient in an acoustic equation by arbitrary boundary observation

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• 作者：Mourad Bellassoued and Masahiro Yamamoto
• 关键词：Stability ; Inverse problem ; FBI transform
• 刊名：Journal des Mathematiques Pures et Appliquees
• 出版年：2006
• 出版时间：February 2006
• 年：2006
• 卷：85
• 期：2
• 页码：193-224
• 全文大小：223 K

文摘

We study the global stability in determination of a coefficient in an acoustic equation from data of the solution in a subboundary over a time interval. Providing regular initial data and values of coefficients in a neighbourhood of the boundary, without any assumption on an observation subboundary, we prove the logarithmic stability estimate in the inverse problem with a single measurement. Moreover the exponent in the stability estimate depends on the regularity of initial data.