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Journal of Dynamical Systems and Geometric Theories

(Since 2002)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X

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Half-Yearly Journal: Publishes research on dynamical systems and geometry, including Random Dynamical Systems, hyperbolic behaviour, complex geometry and Ergodic theory.

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Journal of Dynamical Systems and Geometric Theories
Open Access Original Articles

Determining Functionals for the Strongly Damped Nonlinear Wave Equation

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pp. 105–116Vol. 5Issue 2November 2007DOI: 10.1080/1726037X.2007.10698530XML
Received:
25 Aug 2006
Published Online:
03 Jun 2013
Article type:
Original Articles
Language:
EN
Article no.:
1726037X.2007.10698530
Pages:
105–116

Abstract

We consider the existence of a wide collection of finite sets of functionals on the phase space that completely determines asymptotic behavior of solutions to the strongly damped nonlinear wave equation. The proof makes use of energy methods and the concept of the completeness defect. We also show that the number of determining nodes is two, that is, the asymptotic behavior of solutions is determined by the values of two sufficiently close points in the interval [0, 1].

Keywords

Nonlinear wave equationStrong damping termAsymptotic behaviorCompleteness defect

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