Optimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains
Yannick Privat, Emmanuel Trélat, Enrique Zuazua (2016)
Journal of the European Mathematical Society
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We consider the wave and Schrödinger equations on a bounded open connected subset 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 of during a time interval with . It is well known that, if the pair satisfies the Geometric Control Condition ( being an open set), then an observability inequality holds guaranteeing that the total energy of solutions...