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July/August 2009 Convergence to equilibrium for second order differential equations with weak damping of memory type
Rico Zacher
Adv. Differential Equations 14(7/8): 749-770 (July/August 2009).

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.

Citation

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Rico Zacher. "Convergence to equilibrium for second order differential equations with weak damping of memory type." Adv. Differential Equations 14 (7/8) 749 - 770, July/August 2009.

Information

Published: July/August 2009
First available in Project Euclid: 18 December 2012

zbMATH: 1190.45007
MathSciNet: MR2527692

Subjects:
Primary: 45G05, 45M05

Rights: Copyright © 2009 Khayyam Publishing, Inc.

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Vol.14 • No. 7/8 • July/August 2009
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