Large energy simple modes for a class of Kirchhoff equations

Large energy simple modes for a class of Kirchhoff equations

It is well known that the Kirchhoff equation admits infinitely many simple modes, i.e., time periodic solutions with only one Fourier component in the space variable(s). We prove that for some form of the nonlinear term these simple modes are stable provided that their energy is large enough. Here s...

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Bibliographic Details
Main Author: Marina Ghisi
Format: Article
Language:English
Published: Texas State University 2003-09-01
Series:Electronic Journal of Differential Equations
Subjects:
Kirchhoff equations
orbital stability
Hamiltonian systems
Poincare map
KAM theory.
Online Access:http://ejde.math.txstate.edu/Volumes/2003/96/abstr.html
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spelling doaj-ede671ff9a9e42639c87803895de84832020-11-25T01:40:44ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912003-09-01200396124Large energy simple modes for a class of Kirchhoff equationsMarina GhisiIt is well known that the Kirchhoff equation admits infinitely many simple modes, i.e., time periodic solutions with only one Fourier component in the space variable(s). We prove that for some form of the nonlinear term these simple modes are stable provided that their energy is large enough. Here stable means orbitally stable as solutions of the two-modes system obtained considering initial data with two Fourier components. http://ejde.math.txstate.edu/Volumes/2003/96/abstr.htmlKirchhoff equationsorbital stabilityHamiltonian systemsPoincare mapKAM theory.
collection DOAJ
language English
format Article
sources DOAJ
author Marina Ghisi
spellingShingle Marina Ghisi
Large energy simple modes for a class of Kirchhoff equations
Electronic Journal of Differential Equations
Kirchhoff equations
orbital stability
Hamiltonian systems
Poincare map
KAM theory.
author_facet Marina Ghisi
author_sort Marina Ghisi
title Large energy simple modes for a class of Kirchhoff equations
title_short Large energy simple modes for a class of Kirchhoff equations
title_full Large energy simple modes for a class of Kirchhoff equations
title_fullStr Large energy simple modes for a class of Kirchhoff equations
title_full_unstemmed Large energy simple modes for a class of Kirchhoff equations
title_sort large energy simple modes for a class of kirchhoff equations
publisher Texas State University
series Electronic Journal of Differential Equations
issn 1072-6691
publishDate 2003-09-01
description It is well known that the Kirchhoff equation admits infinitely many simple modes, i.e., time periodic solutions with only one Fourier component in the space variable(s). We prove that for some form of the nonlinear term these simple modes are stable provided that their energy is large enough. Here stable means orbitally stable as solutions of the two-modes system obtained considering initial data with two Fourier components.
topic Kirchhoff equations
orbital stability
Hamiltonian systems
Poincare map
KAM theory.
url http://ejde.math.txstate.edu/Volumes/2003/96/abstr.html
work_keys_str_mv AT marinaghisi largeenergysimplemodesforaclassofkirchhoffequations
_version_ 1725043820536528896

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