An infinite dimensional Duffing-like evolution equation with linear dissipation and an asymptotically small source term

We consider an abstract nonlinear second order evolution equation, inspired by some models for damped oscillations of a beam subject to external loads or magnetic fields, and shaken by a transversal force. When there is no external force, the system has three stationary positions, two stable and one...

Full description

Saved in:
Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 43; pp. 167 - 191
Main Authors Ghisi, Marina, Gobbino, Massimo, Haraux, Alain
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Ltd 01.10.2018
Elsevier BV
Elsevier
Subjects
Online AccessGet full text
ISSN1468-1218
1878-5719
DOI10.1016/j.nonrwa.2018.02.007

Cover

More Information
Summary:We consider an abstract nonlinear second order evolution equation, inspired by some models for damped oscillations of a beam subject to external loads or magnetic fields, and shaken by a transversal force. When there is no external force, the system has three stationary positions, two stable and one unstable, and all solutions are asymptotic for t large to one of these stationary solutions. We show that this pattern extends to the case where the external force is bounded and small enough, in the sense that solutions can exhibit only three different asymptotic behaviors.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2018.02.007