We prove the existence of small amplitude periodic solutions, for a large Lebesgue measure set of frequencies, in the nonlinear beam equation with a weak quadratic and velocity dependent nonlinearity and with Dirichelet boundary conditions. Such nonlinear PDE can be regarded as a simple model describing oscillations of flexible structures like suspension bridges in presence of an uniform wind flow. The periodic solutions are explicitly constructed by a convergent perturbative expansion which can be considered the analogue of the Lindstedt series expansion for the invariant tori in classical mechanics. The periodic solutions are defined only in a Cantor set, and resummation techniques of divergent powers series are used in order to control the small divisors problem.
Mastropietro, V., & Procesi, M. (2006). Lindstedt series for periodic solutions of beam equations with quadratic and velocity dependent nonlinearities. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 5(1), 1-28.
Tipologia: | Articolo su rivista |
Citazione: | Mastropietro, V., & Procesi, M. (2006). Lindstedt series for periodic solutions of beam equations with quadratic and velocity dependent nonlinearities. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 5(1), 1-28. |
URL: | arXiv:math/0505283v1 |
IF: | Con Impact Factor ISI |
Lingua: | English |
Settore Scientifico Disciplinare: | Settore MAT/07 - Fisica Matematica |
Revisione (peer review): | Sì, ma tipo non specificato |
Tipo: | Articolo |
Rilevanza: | Rilevanza internazionale |
Digital Object Identifier (DOI): | http://dx.doi.org/10.3934/cpaa.2006.5.1 |
Stato di pubblicazione: | Pubblicato |
Data di pubblicazione: | 2006 |
Titolo: | Lindstedt series for periodic solutions of beam equations with quadratic and velocity dependent nonlinearities |
Autori: | |
Autori: | Mastropietro, V; Procesi, M |
Appare nelle tipologie: | 01 - Articolo su rivista |