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Comportement à l'infini pour certains systèmes dissipatifs non linéaires

Published online by Cambridge University Press:  14 November 2011

A. Haraux
A. Haraux
Affiliation:
Université Pierre et Marie Curie, Laboratoire d'Analyse Numérique, Paris
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Synopsis

In the Hilbert space framework, we give some results concerning the behaviour when t goes to infinity for solutions of equations of the form:

A is assumed to be a maximal monotone operator and F(t) is a periodic function.

When F = 0, under a compactness assumption for trajectories of (1), we give the complete description of the asymptotic behaviour, e.g. every trajectory is asymptotic to an almost-periodic solution of (1). When F ≠ cst, the compactness hypothesis being too restrictive, we concentrate our efforts on the case of the equation:

with Dirichlet boundary condition) and get weak convergence to particular solutions of the equation when β is either univalued or strictly monotone. The methods used in these cases seem of general interest for hyperbolic equations of dissipative type with periodic forcing term.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 84 , Issue 3-4 , 1979 , pp. 213 - 234
Copyright
Copyright © Royal Society of Edinburgh 1979

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