GLOBAL UNIQUENESS AND STABILITY IN DETERMINING COEFFICIENTS OF WAVE EQUATIONS

By Oleg Yu. Imanuvilov, Masahiro Yamamoto. 2001

196 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/7e957d985ce88f460c8178209ec2d35416449470

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Citations in the corpus

Inverse source problem for the hyperbolic equation with a time-dependent principal part (2015, unknown): “Motivated by the global Lipschitz stability obtained in [13,14] for the inverse source problem for wave equations, in this paper we investigate the same problem for the general hyperbolic equation with time-dependent principal part.”
Uniqueness and stability in determining the speed of propagation of second-order hyperbolic equation with variable coefficients (2004, unknown): “For suitable ! and T>0, Immanuvilov and Yamamoto’s result [7] gives an stability estimate of Hölder type.”
Uniqueness and stability in an inverse problem for the Schrödinger equation (2007, background): “They are related to the same kind of inverse problems of determining a potential, some of them ([10], [13]) with a Dirichlet boundary data and a Neumann measurement and others with a Neumann boundary data and a Dirichlet measurement ([5], [6]).”
Carleman estimates for the non-stationary Lamé system and the application to an inverse problem (2005, result): “As for the corresponding results on the stability for inverse problems for scalar hyperbolic equations, we refer to [22–24] for example.”
An inverse problem for the dynamical Lamé system with two sets of boundary data (2003, unknown): “4 Proof of Main Theorem 2.1 We will combine the method of Bukhgeim and Klibanov [3], its modification by Imanuvilov and Yamamoto [12], and the Carleman estimate (3.1) for the elasticity system.”
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].”
Lipschitz stability for a hyperbolic inverse problem by finite local boundary data (2006, methodology): “A Carleman estimate was first applied to inverse problems by Bukhgeim and Klibanov [3], and see also [2,10,15,16].”
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.”
The seismic reflection inverse problem (2009, background): “For example, recent years have seen a flowering of work on inverse problems for wave equations from the purely mathematical point of view—see for example Belishev (2007), Stefanov and Uhlmann (2005), Imanuvilov and Yamamoto (2001).”
Global uniqueness for a coefficient inverse problem for the non-stationary transport equation via Carleman estimate (2008, background): “A variety of works with uniqueness and stability results for coefficient inverse problems w ere published, which are based on the idea of [4] and [13]-[15], see, for example, Bellassoued [2], [3], Imanuvilov and Yamamoto [9], [ 10 ] and [11] for the case of hyperbolic equations.”
Global Carleman Estimates for Waves and Applications (2011, methodology): “We will first prove Carleman estimates similar to the ones of Theorems 1.1–1.2 for the operator , corresponding to a potential equal to zero.”