Spectral theory of pseudo-differential operators of degree 0 and application to forced linear waves
Résumé
We extend the results of our paper "Attractors for two dimensional waves with homogeneous Hamiltonians of degree 0"
written with Laure Saint-Raymond to the case of forced linear wave equations in any dimension. We prove that, in dimension 2,
if the foliation on the boundary at infinity of the energy shell is
Morse-Smale, we can apply Mourre's theory and hence get
the asymptotics of the forced solution. We also characterize the wavefrontsets of the limit Schwartz distribution
using radial propagation estimates.
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