Almost periodic solutions for a weakly dissipated hybrid system

Sorin Micu; Ademir F. Pazoto

doi:10.3934/mcrf.2014.4.101

Article Contents

2014, Volume 4, Issue 1: 101-113. Doi: 10.3934/mcrf.2014.4.101

This issue Previous Article Control of a Korteweg-de Vries equation: A tutorial Next Article Algebraic characterization of autonomy and controllability of behaviours of spatially invariant systems

Almost periodic solutions for a weakly dissipated hybrid system

Sorin Micu^1, and
Ademir F. Pazoto^2,

1.
Universitatea din Craiova, Craiova 200585
2.
Institute of Mathematics, Federal University of Rio de Janeiro, UFRJ, P.O. Box 68530, CEP 21941-909, Rio de Janeiro, RJ

Received: April 30, 2012

Revised: December 31, 2012

Published: February 2014

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Abstract

We consider a hybrid system coupling an elastic string with a rigid body at one end and we study the existence of an almost periodic solution when an almost periodic force $f$ acts on the body. The weak dissipation of the system does not allow to show the relative compactness of the trajectories which generally implies the existence of such solutions. Instead, we use Fourier analysis to show that the existence or not of the almost periodic solutions depends on the regularity and the exponents of the almost periodic nonhomogeneous term $f$.

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Mathematics Subject Classification: Primary: 35B15; Secondary: 93D20.

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