In this paper we study the long-term dynamics of a doubly nonlinear abstract system which involves a single differential operator to different powers. For a special choice of the nonlinear terms, the system describes the motion of a suspension bridge where the road bed and the main cable are modeled as a nonlinear beam and a vibrating string, respectively, and their coupling is carried out by nonlinear springs. The set of stationary solutions turns out to be nonempty and bounded. As the external loads vanish, the null solution of the system is proved to be exponentially stable provided that the axial load does not exceed some critical value. Finally, we prove the existence of a bounded global attractor of optimal regularity in connection with an arbitrary axial load and quite general nonlinear terms.

Asymptotic dynamics of nonlinear coupled suspension bridge equations

GIORGI, Claudio;VUK, Elena
2013-01-01

Abstract

In this paper we study the long-term dynamics of a doubly nonlinear abstract system which involves a single differential operator to different powers. For a special choice of the nonlinear terms, the system describes the motion of a suspension bridge where the road bed and the main cable are modeled as a nonlinear beam and a vibrating string, respectively, and their coupling is carried out by nonlinear springs. The set of stationary solutions turns out to be nonempty and bounded. As the external loads vanish, the null solution of the system is proved to be exponentially stable provided that the axial load does not exceed some critical value. Finally, we prove the existence of a bounded global attractor of optimal regularity in connection with an arbitrary axial load and quite general nonlinear terms.
File in questo prodotto:
File Dimensione Formato  
JMAA_BGV.pdf

accesso aperto

Tipologia: Full Text
Licenza: DRM non definito
Dimensione 444.57 kB
Formato Adobe PDF
444.57 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11379/225304
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 24
  • ???jsp.display-item.citation.isi??? 22
social impact