Finite dimensional exponential attractors for semilinear wave equations with damping

A. Eden; A. J. Milani; B. Nicolaenko

doi:10.1016/0022-247X(92)90087-T

Finite dimensional exponential attractors for semilinear wave equations with damping

A. Eden
, A. J. Milani
, B. Nicolaenko

Mathematics & Statistical Sciences

Research output: Contribution to journal › Article › peer-review

38 Citations (Scopus)

Abstract

We consider the initial value problem for a class of second order evolution equations that includes, among others, the 3D sine-Gordon equation with damping and the 3D Klein-Gordon type equations with damping. We show the existence of a set with finite fractal dimension that contains the global attractor and attracts all smooth solutions at an exponential rate.

Original language	English
Pages (from-to)	408-419
Number of pages	12
Journal	Journal of Mathematical Analysis and Applications
Volume	169
Issue number	2
DOIs	https://doi.org/10.1016/0022-247X(92)90087-T
Publication status	Published - Sept 15 1992

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/0022-247X(92)90087-T

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title = "Finite dimensional exponential attractors for semilinear wave equations with damping",

abstract = "We consider the initial value problem for a class of second order evolution equations that includes, among others, the 3D sine-Gordon equation with damping and the 3D Klein-Gordon type equations with damping. We show the existence of a set with finite fractal dimension that contains the global attractor and attracts all smooth solutions at an exponential rate.",

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AU - Eden, A.

AU - Milani, A. J.

AU - Nicolaenko, B.

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N2 - We consider the initial value problem for a class of second order evolution equations that includes, among others, the 3D sine-Gordon equation with damping and the 3D Klein-Gordon type equations with damping. We show the existence of a set with finite fractal dimension that contains the global attractor and attracts all smooth solutions at an exponential rate.

AB - We consider the initial value problem for a class of second order evolution equations that includes, among others, the 3D sine-Gordon equation with damping and the 3D Klein-Gordon type equations with damping. We show the existence of a set with finite fractal dimension that contains the global attractor and attracts all smooth solutions at an exponential rate.

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EP - 419

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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ER -

Finite dimensional exponential attractors for semilinear wave equations with damping

Abstract

All Science Journal Classification (ASJC) codes

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