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Séminaire de Physique Mathématique - EDP

Responsable : David Lannes

  • Le 19 octobre 2021 à 11:00
  • Salle 285
    Victor Arnaiz (Orsay)
    Sharp resolvent estimates for damped Baouendi-Grushin operators on the torus
    In this talk I will consider the damped-wave equation associated with the Baouendi-Grushin operator on the two-dimensional flat torus. I will show new semiclassical resolvent estimates for the corresponding non-selfadjoint operator associated with this evolution problem, detailing the effect of sub-ellipticity in connection with the geometry of the damping region and the regularity of the damping term. As a corollary, sharp energy decay rates of solutions of the damped-wave equation are obtained and some differencies with respect to the elliptic Laplacian are exhibited. The method of proof is based on the study of two-microlocal semiclassical measures, normal-form reductions and construction of quasimodes via propagation of time-dependent solutions within the damping region.

    Les séminaires depuis 2013