A VISCOELASTIC PLATE EQUATION WITH A VERY GENERAL KERNEL

Adel M. Al-Mahdi

A VISCOELASTIC PLATE EQUATION WITH A VERY GENERAL KERNEL

Adel M. Al-Mahdi^*

^*Corresponding author for this work

Preparatory Year Program

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

1 Scopus citations

Abstract

The stabilization of the following problem: u_tt − σ∆u_tt + ∆²u − ∫_t k(t − s)∆²u(s)ds = 0, x ∈ Ω, t > 0, 0 is investigated under very general assumption on the relaxation function k. With this general assumption, k′ (t) ≤ −γ(t)Ψ(k(t)), we establish general and optimal decay rate results from which we recover the optimal rates when Ψ(s) = s^p and p covers the full admissible range [1, 2). Our results improve and generalize many earlier results in the literature.

Original language	English
Pages (from-to)	361-379
Number of pages	19
Journal	Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
Volume	27
Issue number	6
State	Published - 2020

Bibliographical note

Publisher Copyright:
© 2020 Watam Press.

Keywords

Convexity
Kernels
Optimal decay
Plate equation
Viscoelastic

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

Cite this

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title = "A VISCOELASTIC PLATE EQUATION WITH A VERY GENERAL KERNEL",

abstract = "The stabilization of the following problem: utt − σ∆utt + ∆2u − ∫t k(t − s)∆2u(s)ds = 0, x ∈ Ω, t > 0, 0 is investigated under very general assumption on the relaxation function k. With this general assumption, k′ (t) ≤ −γ(t)Ψ(k(t)), we establish general and optimal decay rate results from which we recover the optimal rates when Ψ(s) = sp and p covers the full admissible range [1, 2). Our results improve and generalize many earlier results in the literature.",

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T1 - A VISCOELASTIC PLATE EQUATION WITH A VERY GENERAL KERNEL

AU - Al-Mahdi, Adel M.

PY - 2020

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N2 - The stabilization of the following problem: utt − σ∆utt + ∆2u − ∫t k(t − s)∆2u(s)ds = 0, x ∈ Ω, t > 0, 0 is investigated under very general assumption on the relaxation function k. With this general assumption, k′ (t) ≤ −γ(t)Ψ(k(t)), we establish general and optimal decay rate results from which we recover the optimal rates when Ψ(s) = sp and p covers the full admissible range [1, 2). Our results improve and generalize many earlier results in the literature.

AB - The stabilization of the following problem: utt − σ∆utt + ∆2u − ∫t k(t − s)∆2u(s)ds = 0, x ∈ Ω, t > 0, 0 is investigated under very general assumption on the relaxation function k. With this general assumption, k′ (t) ≤ −γ(t)Ψ(k(t)), we establish general and optimal decay rate results from which we recover the optimal rates when Ψ(s) = sp and p covers the full admissible range [1, 2). Our results improve and generalize many earlier results in the literature.

KW - Convexity

KW - Kernels

KW - Optimal decay

KW - Plate equation

KW - Viscoelastic

UR - https://www.scopus.com/pages/publications/85131072837

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JO - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

JF - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

IS - 6

ER -

A VISCOELASTIC PLATE EQUATION WITH A VERY GENERAL KERNEL

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this