Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent

A. Kh. Khanmamedov

doi:10.3934/dcds.2011.31.119

Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent

A. Kh. Khanmamedov

Division of Applied Mathematics

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

7 Citations (Scopus)

Abstract

In this paper the long time behaviour of the solutions of the 3-D strongly damped wave equation is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H ¹ ₀ (ω) × L ₂(ω) and then it is proved that this is also a global attractor in (H ²(ω)H ¹ ₀(ω) ×H ¹ ₀(ω).

Original language	English
Pages (from-to)	119-138
Number of pages	20
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	31
Issue number	1
DOIs	https://doi.org/10.3934/dcds.2011.31.119
Publication status	Published - Sept 2011

Keywords

Attractors
Strongly damped wave equations

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title = "Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent",

abstract = "In this paper the long time behaviour of the solutions of the 3-D strongly damped wave equation is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H 1 0 (ω) × L 2(ω) and then it is proved that this is also a global attractor in (H 2(ω)H 1 0(ω) ×H 1 0(ω).",

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year = "2011",

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doi = "10.3934/dcds.2011.31.119",

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AB - In this paper the long time behaviour of the solutions of the 3-D strongly damped wave equation is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H 1 0 (ω) × L 2(ω) and then it is proved that this is also a global attractor in (H 2(ω)H 1 0(ω) ×H 1 0(ω).

KW - Attractors

KW - Strongly damped wave equations

UR - https://www.scopus.com/pages/publications/84859568319

U2 - 10.3934/dcds.2011.31.119

DO - 10.3934/dcds.2011.31.119

M3 - Article

AN - SCOPUS:84859568319

SN - 1078-0947

VL - 31

SP - 119

EP - 138

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 1

ER -

Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent

Abstract

Keywords

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