Carleman estimates for coefficient inverse problems and numerical applications

By Michael V. Klibanov, A. Timonov. 2004

437 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/303bcb4179334f19545b3c36aaac89ef1d1e0e9c

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In Computational Theory and Mathematics

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Citations in the corpus

Stability estimate for the hyperbolic inverse boundary value problem by local Dirichlet-to-Neumann map (2008, methodology): “In order to extend the estimate on the conic subset to an estimate on the ball, we use an idea of Heck and Wang [10] and conditional stability for analytic continuation established by Vessella [32].”
Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems (2012, methodology): “4 of the book of Klibanov and Timonov [86] as well as in the paper of Clason and Klibanov [44].”
Lipschitz stability in the determination of the principal part of a parabolic equation (2009, methodology): “As for inverse problems of determining coefficients in parabolic equations, we refer to Danilaev [11], Elayyan and Isakov [12], Imanuvilov and Yamamoto [20,22], Isakov [25], Isakov and Kindermann [26], Ivanchov [27], Klibanov [30], Klibanov and Timonov [32], Yamamoto and Zou [41].”
About stability and regularization of ill-posed elliptic Cauchy problems: the case of Lipschitz domains (2010, methodology): “4 Application to the method of quasi-reversibility In this section, we use the stability estimates obtained in previous section to derive a convergence rate for the quasi-reversibility method, and therefore to complete the results already obtained in [4, 11].”
Inverse source problem for the hyperbolic equation with a time-dependent principal part (2015, neutral): “Regarding the numerical approaches to co-eﬃcient inverse hyperbolic problems and related topics, we refer to the two monographs [18,20].”
The Wave Equation: Control and Numerics (2012, neutral): “We refer, for instance, to the works of Bukgheim and Klibanov [13] and the books [12, 58, 56, 59] (and the references therein) for a presentation of the state of the art in that field.”
Inverse problem for a parabolic system with two components by measurements of one component (2008, background): “For hyperbolic problems, among many works, we restrict ourselves to a few works such as [9,10,12,14,15] and see the references also in [9] and [12].”
Carleman estimate for a fractional diffusion equation with half order and application (2011, background): “See also [13] as source book on the Carleman estimate and applications.”