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Observability properties of the homogeneous wave equation on a closed manifold

2019
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Communications in Partial Differential Equations
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We consider the wave equation on a closed Riemannian manifold. We observe the restriction of the solutions to a measurable subset ω along a time interval [0, T ] with T > 0. It is well known that, if ω is open and if the pair (ω, T ) satisfies the Geometric Control Condition then an observability inequality is satisfied, comparing the total energy of solutions to their energy localized in ω × (0, T ). The observability constant C T (ω) is then defined as the infimum over the set of all

doi:10.1080/03605302.2019.1581799
fatcat:2l7mi5zw3rf55is3bg3w5ztgm4