Stability estimate for a hyperbolic inverse problem with time-dependent coefficient. (18th November 2015)

• Record Type: Journal Article
• Authors: Aïcha, Ibtissem Ben
• Is Part Of: Inverse problems. Volume 31:Number 12(2015:Dec.)
• Publication Date: 2015-11-18
• Subjects: inverse problems -- wave equation -- Dirichlet-to-Neumann map; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/12/125010
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We study the stability issue in the inverse problem of determining the time-dependent coefficient of order zero appearing in the wave equation, from boundary observations. In dimension we derive a log-type stability estimate with respect to the Dirichlet-to-Neumann map for the restriction of q to a suitable subset of the domain. This is provided q is known outside the above subset. Moreover, by enlarging the set of data, we prove that q can be stably retrieved in larger subsets of the domain, including the whole domain itself.