Stability estimate for the hyperbolic inverse boundary value problem by local Dirichlet-to-Neumann map
By Mourad Bellassoued *, D. Jellali, Masahiro Yamamoto. 2008
51 citations recorded by the source corpus.
Abstract In this paper we consider the stability of the inverse problem of determining a function q ( x ) in a wave equation ∂ t 2 u − Δ u + q ( x ) u = 0 in a bounded smooth domain in R n from boundary observations. This information is enclosed in the hyperbolic (dynamic) Dirichlet-to-Neumann map associated to the solutions to the wave equation. We prove in the case of n ⩾ 2 that q ( x ) is uniquely determined by the range restricted to a subboundary of the Dirichlet-to-Neumann map whose stability is a type of double logarithm.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0e8893fa730e88d23e9707e49f473313893194d2
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Stability estimate for hyperbolic inverse problem with time dependent coefficient (2015, methodology): “Kian [12], indeed, inspired by Bellassoued-Jellali-Yamammoto [2]-[1] and using suitable complex geometric optics solutions and Carleman estimate, he proved a log-log type stability estimate in determining the time dependent coefficient q(t, x), from the knowledge of partial Dirichlet-to-Neumann meas”