Global Lipschitz stability in an inverse hyperbolic problem by interior observations

By Oleg Yu. Imanuvilov, Masahiro Yamamoto. 2001

216 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c77e43ed7fabab6e19cb2e8b1579d9d0e3e8bdcb

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Citations in the corpus

An inverse problem for the dynamical Lamé system with two sets of boundary data (2003, methodology): “[25] Yamamoto, M. Uniqueness and stability in multidimensional hyperbolic inverse problems.”
Inverse problem for a parabolic system with two components by measurements of one component (2008, methodology): “23], [24] Klibanov and Timonov [26], Yuan and Yamamoto [32] and the references therein. For hyperbolic problems, among many works, we restrict ourselves to a few works such as Imanuvilov and Yamamoto [16], Isakov [20], [21], Klibanov [23], Klibanov and Timonov [26] and see the references also in Isa”
Carleman estimates for the non-stationary Lamé system and the application to an inverse problem (2005, methodology): “The Carleman estimate for the non-stationary Lamé equation was obtained for functions with compact supports, by Eller, Isakov, Nakamura and Tataru [13], Ikehata, Nakamura and Yamamoto [16], Imanuvilov, Isakov and Yamamoto [19], Isakov [28], and, by the methodology by [8] or [22], several uniqueness ”
Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems (2012, methodology): “ndition u1 |ST = u2 |ST = P |ST .It was shown in [131] that if Ω = {|x| <R} and T>2R,then kfkH3(Ω) ≤ C X4 j=0 ∂j t g 2 L2(ST ) 1/2 . Isakov and Yamamoto [64] and Imanuvilov and Yamamoto [60, 61] have obtained various Lipschitz stability estimates for MCIPs for hyperbolic PDEs with the prin”
Monotonicity-based inversion of the fractional Schr\"odinger equation (2017, background): “Lipschitz stability (that was already utilized in [37, 33, 67]), diﬀers from traditional approaches that are mostly based on quantitative unique continuation or quantitative Runge approximation, cf., [52, 2, 48, 49, 19, 5, 7, 10, 54, 53, 11, 68, 73, 74, 14, 13, 60, 4, 12, 9, 3, 66]. Our new approach”
Lipschitz stability in the determination of the principal part of a parabolic equation (2009, methodology): “[24] O.Yu. Imanuvilov and M. Yamamoto, Carleman inequalities for parabolic equations in Sobolev spaces of negative order and exact controllability for semilinear parabolic equations.”
Carleman estimates for parabolic equations and applications (2009, methodology): “Yamamoto and Zou [143] proved the Lipschitz stability in determining c(x), x ∈ and for it, the assumption u(x, t0) > 0 for x ∈ is essential.”
Inverse source problem for the hyperbolic equation with a time-dependent principal part (2015, unknown): “We refer to Bukhgeim and Klibanov [5] for the uniqueness, and Yamamoto [28,29], Puel and Yamamoto [27], Isakov and Yamamoto [16], Imanuvilov and Yamamoto [13, 14] for the stability.”