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The Dirichlet-to-Neumann map for a semilinear wave equation on Lorentzian manifolds (2103.08110v1)

Published 15 Mar 2021 in math.AP

Abstract: We consider the semilinear wave equation $\Box_g u+a u4=0$, $a\neq 0$, on a Lorentzian manifold $(M,g)$ with timelike boundary. We show that from the knowledge of the Dirichlet-to-Neumann map one can recover the metric $g$ and the coefficient $a$ up to natural obstructions. Our proof rests on the analysis of the interaction of distorted plane waves together with a scattering control argument, as well as Gaussian beam solutions.

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