Decay rates for the damped wave equation on the torus
Nalini Anantharaman,
Matthieu Léautaud,
Stéphane Nonnenmacher
Abstract:We address the decay rates of the energy for the damped wave equation when the damping coefficient b does not satisfy the Geometric Control Condition (GCC). First, we give a link with the controllability of the associated Schrödinger equation. We prove in an abstract setting that the observability of the Schrödinger group implies that the semigroup associated to the damped wave equation decays at rate 1/ √ t (which is a stronger rate than the general logarithmic one predicted by the Lebeau Theorem).Second, we … Show more
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