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Article Dans Une Revue Analysis & PDE Année : 2019

Spectral theory of pseudo-differential operators of degree 0 and application to forced linear waves

Yves Colin de Verdìère

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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Dates et versions

hal-01761011 , version 1 (07-04-2018)
hal-01761011 , version 2 (13-05-2019)

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Yves Colin de Verdìère. Spectral theory of pseudo-differential operators of degree 0 and application to forced linear waves. Analysis & PDE, 2019, 13 (5), pp.1521-1537. ⟨10.2140/apde.2020.13.1521⟩. ⟨hal-01761011v2⟩
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