FM 20-05; cond-mat/0507686

Authors: Vieri Mastropietro, Michela Procesi

Title Lindstedt series for periodic solutions of beam equations with quadratic and nonlinear dependent nonlinearities

Abstract: We prove the existence of small amplitude periodic solutions, for a large Lebesgue measure set, in the nonlinear beam equation with a weak quadratic and velocity dependent nonlinearity and with Direchelet 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 explicitely constructed by a convergent perturbative expansion which can be considered the analogue of the lindstedt series for the invariant tori in classical mechanics. The periodic solutions are defined only in a Cantor set, and resummation techniques of divergent power series are used in order to control the small divisor problem.

Key words:  Small divisors, PDE

Vieri Mastropietro
Matematica, Universita' di Roma 2
V.le della Ricerca Scientifica
00133 Roma, Italia
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