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2020 Spectral theory of pseudodifferential operators of degree 0 and an application to forced linear waves
Yves Colin de Verdière
Anal. PDE 13(5): 1521-1537 (2020). DOI: 10.2140/apde.2020.13.1521

Abstract

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 wavefront sets of the limit Schwartz distribution using radial propagation estimates.

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Yves Colin de Verdière. "Spectral theory of pseudodifferential operators of degree 0 and an application to forced linear waves." Anal. PDE 13 (5) 1521 - 1537, 2020. https://doi.org/10.2140/apde.2020.13.1521

Information

Received: 9 May 2018; Revised: 6 April 2019; Accepted: 12 May 2019; Published: 2020
First available in Project Euclid: 17 September 2020

zbMATH: 07271837
MathSciNet: MR4149069
Digital Object Identifier: 10.2140/apde.2020.13.1521

Subjects:
Primary: 35B34 , 35Q30 , 35Q35 , 58J40 , 76B55
Secondary: 76B70

Keywords: attractors , escape functions , forced waves , inertial waves , internal waves , limiting absorption principle , Morse–Smale property , Mourre theory , pseudodifferential operator , Spectral theory

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 5 • 2020
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