Geodesic
Optimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains
Journal of the European Mathematical Society, Tome 18 (2016) no. 5, pp. 1043-1111

Voir la notice de l'article provenant de la source EMS Press

We consider the wave and Schrödinger equations on a bounded open connected subset Ω of a Riemannian manifold, with Dirichlet, Neumann or Robin boundary conditions whenever its boundary is nonempty. We observe the restriction of the solutions to a measurable subset ω of Ω during a time interval [0,T] with T>0. It is well known that, if the pair (ω,T) satisfies the Geometric Control Condition (ω being an open set), then an observability inequality holds guaranteeing that the total energy of solutions can be estimated in terms of the energy localized in ω×(0,T).
DOI : 10.4171/jems/608
Classification : 35-XX, 49-XX, 58-XX, 93-XX
Keywords: Wave equation, Schrödinger equation, observability inequality, optimal design, spectral decomposition, ergodic properties, quantum ergodicity 
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     author = {Yannick Privat and Emmanuel Tr\'elat and Enrique Zuazua},
     title = {Optimal observability of the multi-dimensional wave and {Schr\"odinger} equations in quantum ergodic domains},
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     pages = {1043--1111},
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Yannick Privat; Emmanuel Trélat; Enrique Zuazua. Optimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains. Journal of the European Mathematical Society, Tome 18 (2016) no. 5, pp. 1043-1111. doi: 10.4171/jems/608

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