Alexandre Cabot, Hans Engler, Sebastien Gadat
Abstract:
We investigate the asymptotic properties as
of the differential equation
where
is
-valued,
the map
is non increasing, and
is a potential with locally Lipschitz
continuous derivative. We identify conditions on the function
that guarantee or exclude the convergence of solutions of this problem
to points in
,
in the case where
is
convex and
is an interval. The condition
is known to be necessary for convergence of trajectories. We give a
slightly stronger condition that is sufficient.
Published April 15, 2009.
Math Subject Classifications: 34G20, 34A12, 34D05.
Key Words: Differential equation; dissipative dynamical system;
vanishing damping; asymptotic behavior.
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Alexandre Cabot Département de Mathématiques, Université Montpellier II, CC 051 Place Eugène Bataillon, 34095 Montpellier Cedex 5, France email: acabot@math.univ-montp2.fr |
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Hans Engler Department of Mathematics, Georgetown University Box 571233 Washington, DC 20057, USA email: engler@georgetown.edu |
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Sébastien Gadat Institut de Mathématiques de Toulouse, Université Paul Sabatier 118, Route de Narbonne 31062 Toulouse Cedex 9, France email: Sebastien.Gadat@math.ups-tlse.fr |
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