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A sharp ultimate bound of the solutions to some second-order evolution equations with nonlinear damping

Part of: Representations of solutions Hyperbolic equations and systems General theory in ordinary differential equations Partial differential equations

Published online by Cambridge University Press:  22 July 2015

Faouzia Aloui
Faouzia Aloui*
Affiliation:
UPMC Paris 6, UMR 7598, Laboratoire Jacques Louis Lions, 4 place Jussieu, 75252 Paris Cedex 05, France, (aloui@ann.jussieu.fr)
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Abstract

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We establish a sharp ultimate bound of the solution to a second-order dissipative nonlinear equation with bounded forcing term.

Keywords

second-order equationultimate boundednessbounded forcing term

MSC classification

Primary: 34A34: Nonlinear equations and systems, general 35B40: Asymptotic behavior of solutions
Secondary: 35D30: Weak solutions 35D35: Strong solutions 35L10: Second-order hyperbolic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 4 , August 2015 , pp. 703 - 714
Copyright
Copyright © Royal Society of Edinburgh 2015