Unique recovery of lower order coefficients for hyperbolic equations from data on disjoint sets

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http://hdl.handle.net/10138/332834

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Kian , Y , Kurylev , Y , Lassas , M & Oksanen , L 2019 , ' Unique recovery of lower order coefficients for hyperbolic equations from data on disjoint sets ' , Journal of Differential Equations , vol. 267 , no. 4 , pp. 2210-2238 . https://doi.org/10.1016/j.jde.2019.03.008

Title: Unique recovery of lower order coefficients for hyperbolic equations from data on disjoint sets
Author: Kian, Yavar; Kurylev, Yaroslav; Lassas, Matti; Oksanen, Lauri
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, University College London
Date: 2019-08-05
Language: eng
Number of pages: 29
Belongs to series: Journal of Differential Equations
ISSN: 0022-0396
URI: http://hdl.handle.net/10138/332834
Abstract: We consider a restricted Dirichlet-to-Neumann map Lambda(T)(S, R) associated with the operator partial derivative(2)(t) - Delta(g) + A + q where Delta(g) is the Laplace-Beltrami operator of a Riemannian manifold (M, g), and A and q are a vector field and a function on M. The restriction Lambda(T)(S, R) corresponds to the case where the Dirichlet traces are supported on (0, T) x S and the Neumann traces are restricted on (0, T) x R. Here S and R are open sets, which may be disjoint, on the boundary of M. We show that Lambda(T)(S, R) determines uniquely, up the natural gauge invariance, the lower order terms A and q in a neighborhood of the set R assuming that R is strictly convex and that the wave equation is exactly controllable from S in time T/2. We give also a global result under a convex foliation condition. The main novelty is the recovery of A and q when the sets R and S are disjoint. We allow A and q to be non-self-adjoint, and in particular, the corresponding physical system may have dissipation of energy. Crown Copyright (C) 2019 Published by Elsevier Inc. All rights reserved.
Subject: Inverse problems
Wave equation
Partial data
GELFAND INVERSE PROBLEM
CALDERON PROBLEM
OPERATOR
MANIFOLDS
MAP
111 Mathematics
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