NDLI: Attractors for Second-Order Evolution Equations with a Nonlinear Damping

Content Provider	Springer Nature Link
Author	Chueshov, Igor Lasiecka, Irena
Copyright Year	2004
Abstract	We study long-time dynamics of abstract nonlinear second-order evolution equations with a nonlinear damping. Under suitable hypotheses we prove existence of a compact global attractor and finiteness of its fractal dimension. We also show that any solution is stabilized to an equilibrium and estimate the rate of the convergence which, in turn, depends on the behaviour at the origin of the function describing the dissipation. If the damping is bounded below by a linear function, this rate is exponential. Our approach is based on far reaching generalizations of the Ceron–Lopes theorem on asymptotic compactness and Ladyzhenskaya’s theorem on the dimension of invariant sets. An application of our results to nonlinear damped wave and plate equations allow us to obtain new results pertaining to structure and properties of global attractors for nonlinear waves and plates.
Starting Page	469
Ending Page	512
Page Count	44
File Format	PDF
ISSN	10407294
Journal	Journal of Dynamics and Differential Equations
Volume Number	16
Issue Number	2
e-ISSN	15729222
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2004-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Ordinary Differential Equations Partial Differential Equations Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Analysis

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Attractors for Second-Order Evolution Equations with a Nonlinear Damping