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Recovery of zeroth order coefficients in non-linear wave equations

Feizmohammadi, A; Oksanen, L; (2020) Recovery of zeroth order coefficients in non-linear wave equations. Journal of the Institute of Mathematics of Jussieu 10.1017/S1474748020000122. (In press). Green open access

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Abstract

This paper is concerned with the resolution of an inverse problem related to the recovery of a function V from the source to solution map of the semi-linear equation (square_{g} + V)u + u^{3} on a globally hyperbolic Lorentzian manifold (M,g). We first study the simpler model problem, where (M,g) is the Minkowski space, and prove the unique recovery of V through the use of geometric optics and a three-fold wave interaction arising from the cubic non-linearity. Subsequently, the result is generalized to globally hyperbolic Lorentzian manifolds by using Gaussian beams.

Type: Article
Title: Recovery of zeroth order coefficients in non-linear wave equations
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/S1474748020000122
Publisher version: https://doi.org/10.1017/S1474748020000122
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10111857
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