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A ONE-DIMENSIONAL WAVE EQUATION WITH NONLINEAR DAMPING

Published online by Cambridge University Press:  06 December 2006

STEFANIA GATTI  and
VITTORINO PATA
STEFANIA GATTI
Affiliation:
Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, I-44100 Ferrara, Italy e-mail: stefania.gatti@unife.it
VITTORINO PATA
Affiliation:
Dipartimento di Matematica “F.Brioschi”, Politecnico di Milano, Via Bonardi 9, I-20133 Milano, Italy e-mail: pata@mate.polimi.it
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Abstract

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We consider a one-dimensional weakly damped wave equation, with a damping coefficient depending on the displacement. We prove the existence of a regular connected global attractor of finite fractal dimension for the associated dynamical system, as well as the existence of an exponential attractor.

Keywords

35B4135L0537L2537L45
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 48 , Issue 3 , September 2006 , pp. 419 - 430
Copyright
2006 Glasgow Mathematical Journal Trust