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).
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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 BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10111857 |
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