2017/02/22 by Riccardo Montalto, Montalto, Riccardo · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #35L10 #37K55 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods for differential equations #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math.AP #msc:35L10 #msc:37K55
paper · pdf · doi:10.48550/arxiv.1702.06880
50 pages. version 2. change of the title and other minor changes with respect to the previous version
openalex publication_date 2017/02/22 · arxiv created 2017/08/09 · arxiv updated 2017/08/10 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
We prove a reducibility result for a class of quasi-periodically forced linear wave equations on the d-dimensional torus \mathbbTd of the form ∂tt v - Δv + ε \cal P(ωt)[v] = 0 where the perturbation \cal P(ωt) is a second order operator of the form \cal P(ωt) = - a(ωt) Δ- \cal R(ωt), the frequency ω∈ \cal Rν is in some Borel set of large Lebesgue measure, the function a : \mathbbTν→ \cal R (independent of the space variable) is sufficiently smooth and \cal R(ωt) is a time-dependent finite rank operator. This is the first reducibility result for linear wave equations with unbounded perturbations on the higher dimensional torus \mathbbTd. As a corollary, we get that the linearized Kirchhoff equation at a smooth and sufficiently small quasi-periodic function is reducible.