1. Inverse Problems for Semilinear Wave Equations on Lorentzian Manifolds.
- Author
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Lassas, Matti, Uhlmann, Gunther, and Wang, Yiran
- Subjects
- *
INVERSE problems , *WAVE equation , *MANIFOLDS (Mathematics) , *GEODESICS , *TOPOLOGY , *LATTICE theory - Abstract
We consider inverse problems in space-time (
M ,g ), a 4-dimensional Lorentzian manifold. For semilinear wave equations □gu+H(x,u)=f, where □g denotes the usual Laplace-Beltrami operator, we prove that the source-to-solution map L:f→u|V , where V is a neighborhood of a time-like geodesic μ, determines the topological, differentiable structure and the conformal class of the metric of the space-time in the maximal set, where waves can propagate from μ and return back. Moreover, on a given space-time ( M ,g ), the source-to-solution map determines some coefficients of the Taylor expansion ofH inu . [ABSTRACT FROM AUTHOR]- Published
- 2018
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