Spectral theory of pseudo-differential operators of degree 0 and application to forced linear waves
| Autor: | Yves Colin de Verdière |
|---|---|
| Přispěvatelé: | Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Spectral theory
FOS: Physical sciences Boundary (topology) attractors 35B34 01 natural sciences Mathematics - Spectral Theory Mourre theory Mathematics - Analysis of PDEs inertial waves [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] 0103 physical sciences Attractor forced waves FOS: Mathematics escape functions [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] limiting absorption principle AMS codes: 35Q30 35B34 35Q35 58J40 76B55 76B70 0101 mathematics Spectral Theory (math.SP) Mathematical Physics Mathematics Numerical Analysis Morse-Smale property Applied Mathematics 010102 general mathematics Mathematical analysis pseudodifferential operator 58J40 Mathematical Physics (math-ph) spectral theory Wave equation Differential operator pseudo-differential operator Pseudo-differential operator Foliation Morse–Smale property Distribution (mathematics) 76B55 internal waves 35Q30 010307 mathematical physics 76B70 35Q35 Analysis Analysis of PDEs (math.AP) [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP] |
| Zdroj: | Analysis & PDE Analysis & PDE, Mathematical Sciences Publishers, In press Analysis and PDEs Analysis and PDEs, In press Anal. PDE 13, no. 5 (2020), 1521-1537 |
| ISSN: | 2157-5045 1948-206X |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|