We prove a reducibility result for a class of quasi-periodically forced linear wave equations on the d-dimensional torus Td of the form ∂ttv − v + εP(ωt)[v] = 0, where the perturbation P(ωt) is a second order operator of the form P(ωt) = −a(ωt) − R(ωt), the frequency ω ∈ Rν is in some Borel set of large Lebesgue measure, the function a : Tν → R (independent of the space variable) is sufficiently smooth and 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 Td. As a corollary, we get that the linearized Kirchhoff equation at a smooth and sufficiently small quasi-periodic function is reducible.
A Reducibility Result for a Class of Linear Wave Equations on T-d / R. Montalto. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - :6(2019), pp. 1788-1862.
Titolo: | A Reducibility Result for a Class of Linear Wave Equations on T-d |
Autori: | |
Parole Chiave: | Quasi-periodic solutions; unboun perturbations; global solvability; Kirchhoff equation; kam tori; theorem; NLS |
Settore Scientifico Disciplinare: | Settore MAT/07 - Fisica Matematica Settore MAT/05 - Analisi Matematica |
Data di pubblicazione: | 2019 |
Rivista: | |
Tipologia: | Article (author) |
Data ahead of print / Data di stampa: | 2017 |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1093/imrn/rnx167 |
Appare nelle tipologie: | 01 - Articolo su periodico |
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