Majoration du nombre de résonances près de l'axe réel (d'après un travail avec M. Zworski)
We study the time-harmonic acoustic scattering in a duct in presence of a flow and of a discontinuous impedance boundary condition. Unlike a continuous impedance, a discontinuous one leads to still open modeling questions, as in particular the singularity of the solution at the abrupt transition and the choice of the right unknown to formulate the scattering problem. To address these questions we propose a mathematical approach based on variational formulations set in weighted Sobolev spaces. Considering...
We obtain some microlocal estimates of the resonant states associated to a resonance of an -differential operator. More precisely, we show that the normalized resonant states are