Advances in Differential Equations

Convergence to equilibrium for second order differential equations with weak damping of memory type

Rico Zacher

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Abstract

We study the asymptotic behavior, as $t\to\infty$, of bounded solutions to a second-order integro-differential equation in finite dimensions where the damping term is of memory type and can be of arbitrary fractional order less than 1. We derive appropriate Lyapunov functions for this equation and prove that any global bounded solution converges to an equilibrium of a related equation, if the nonlinear potential ${\mathcal E}$ occurring in the equation satisfies the Łojasiewicz inequality.

Article information

Source
Adv. Differential Equations Volume 14, Number 7/8 (2009), 749-770.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867233

Mathematical Reviews number (MathSciNet)
MR2527692

Zentralblatt MATH identifier
1190.45007

Subjects
Primary: 45G05: Singular nonlinear integral equations 45M05: Asymptotics

Citation

Zacher, Rico. Convergence to equilibrium for second order differential equations with weak damping of memory type. Adv. Differential Equations 14 (2009), no. 7/8, 749--770. https://projecteuclid.org/euclid.ade/1355867233.


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