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arXiv · 2112.09539

Control of waves on Lorentzian manifolds with curvature bounds

Vaibhav Kumar Jena·Arick Shao
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Abstract

We prove boundary controllability results for wave equations (with lower-order terms) on Lorentzian manifolds with time-dependent geometry satisfying suitable curvature bounds. The main ingredient is a novel global Carleman estimate on Lorentzian manifolds that is supported in the exterior of a null (or characteristic) cone, which leads to both an observability inequality and bounds for the corresponding constant. The Carleman estimate also yields a unique continuation result on the null cone exterior, which has applications toward inverse problems for linear waves on Lorentzian backgrounds.

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Vaibhav Kumar Jena, Arick Shao. 2021-12-17. Control of waves on Lorentzian manifolds with curvature bounds. https://doi.org/10.1051/cocv%2F2024056

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