A strong global attractor for the 3D wave equation with displacement dependent damping

A. Kh Khanmamedov

doi:10.1016/j.aml.2010.04.013

A strong global attractor for the 3D wave equation with displacement dependent damping

A. Kh Khanmamedov

Division of Applied Mathematics

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

7 Citations (Scopus)

Abstract

We prove that if the displacement coefficient of the damping of the 3D wave equation is a positive constant on the interval (-l, l), for large enough l < 0, then this equation has a strong global attractor in H¹ ₀(Ω) × L₂(Ω). We also show that this attractor is a bounded subset of H2(Ω) ∩ H₀ ¹(Ω) × H₀¹(Ω).

Original language	English
Pages (from-to)	928-934
Number of pages	7
Journal	Applied Mathematics Letters
Volume	23
Issue number	8
DOIs	https://doi.org/10.1016/j.aml.2010.04.013
Publication status	Published - Aug 2010

Keywords

Attractors
Wave equations

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10.1016/j.aml.2010.04.013

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title = "A strong global attractor for the 3D wave equation with displacement dependent damping",

abstract = "We prove that if the displacement coefficient of the damping of the 3D wave equation is a positive constant on the interval (-l, l), for large enough l < 0, then this equation has a strong global attractor in H1 0(Ω) × L2(Ω). We also show that this attractor is a bounded subset of H2(Ω) ∩ H0 1(Ω) × H01(Ω).",

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N2 - We prove that if the displacement coefficient of the damping of the 3D wave equation is a positive constant on the interval (-l, l), for large enough l < 0, then this equation has a strong global attractor in H1 0(Ω) × L2(Ω). We also show that this attractor is a bounded subset of H2(Ω) ∩ H0 1(Ω) × H01(Ω).

AB - We prove that if the displacement coefficient of the damping of the 3D wave equation is a positive constant on the interval (-l, l), for large enough l < 0, then this equation has a strong global attractor in H1 0(Ω) × L2(Ω). We also show that this attractor is a bounded subset of H2(Ω) ∩ H0 1(Ω) × H01(Ω).

KW - Attractors

KW - Wave equations

UR - https://www.scopus.com/pages/publications/78651362705

U2 - 10.1016/j.aml.2010.04.013

DO - 10.1016/j.aml.2010.04.013

M3 - Article

AN - SCOPUS:78651362705

SN - 0893-9659

VL - 23

SP - 928

EP - 934

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 8

ER -

A strong global attractor for the 3D wave equation with displacement dependent damping

Abstract

Keywords

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