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arXiv · 2103.08110

The Dirichlet-to-Neumann map for a semilinear wave equation on Lorentzian manifolds

Peter Hintz·Gunther Uhlmann·Jian Zhai
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Abstract

We consider the semilinear wave equation $\Box_g u+a u^4=0$, $a\neq 0$, 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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Peter Hintz, Gunther Uhlmann, Jian Zhai. 2021-03-15. The Dirichlet-to-Neumann map for a semilinear wave equation on Lorentzian manifolds. https://arxiv.org/abs/2103.08110

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