Existence and decay of solutions of a viscoelastic equation with a nonlinear source

Said Berrimi; Salim A. Messaoudi

doi:10.1016/j.na.2005.08.015

Existence and decay of solutions of a viscoelastic equation with a nonlinear source

Said Berrimi, Salim A. Messaoudi^*

^*Corresponding author for this work

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

224 Scopus citations

Abstract

In a bounded domain, we consider u_tt- Δu+∫^t₀g(t-τ)Δudτ=|u|γu, where γ>0, and g is a nonnegative and decaying function. We prove a local existence theorem and show, for certain initial data and suitable conditions on g and γ, that this solution is global with energy which decays exponentially or polynomially depending on the rate of the decay of the relaxation function g.

Original language	English
Pages (from-to)	2314-2331
Number of pages	18
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	64
Issue number	10
DOIs	https://doi.org/10.1016/j.na.2005.08.015
State	Published - 15 May 2006
Externally published	Yes

Bibliographical note

Funding Information:
The authors would like to express their sincere thanks to King Fahd University of Petroleum and Minerals for its support. This work has been funded by KFUPM under Project # MS/ VISCO ELASTIC 270.

Keywords

Exponential decay
Global existence
Local existence
Nonlinear source
Polynomial decay
Relaxation function
Viscoelastic

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.na.2005.08.015

Cite this

@article{b7f5bcc6153a434bb05379748fcde84a,

title = "Existence and decay of solutions of a viscoelastic equation with a nonlinear source",

abstract = "In a bounded domain, we consider utt- Δu+∫t0g(t-τ)Δudτ=|u|γu, where γ>0, and g is a nonnegative and decaying function. We prove a local existence theorem and show, for certain initial data and suitable conditions on g and γ, that this solution is global with energy which decays exponentially or polynomially depending on the rate of the decay of the relaxation function g.",

keywords = "Exponential decay, Global existence, Local existence, Nonlinear source, Polynomial decay, Relaxation function, Viscoelastic",

author = "Said Berrimi and Messaoudi, {Salim A.}",

note = "Funding Information: The authors would like to express their sincere thanks to King Fahd University of Petroleum and Minerals for its support. This work has been funded by KFUPM under Project # MS/ VISCO ELASTIC 270.",

year = "2006",

month = may,

day = "15",

doi = "10.1016/j.na.2005.08.015",

language = "English",

volume = "64",

pages = "2314--2331",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

number = "10",

}

TY - JOUR

T1 - Existence and decay of solutions of a viscoelastic equation with a nonlinear source

AU - Berrimi, Said

AU - Messaoudi, Salim A.

N1 - Funding Information: The authors would like to express their sincere thanks to King Fahd University of Petroleum and Minerals for its support. This work has been funded by KFUPM under Project # MS/ VISCO ELASTIC 270.

PY - 2006/5/15

Y1 - 2006/5/15

N2 - In a bounded domain, we consider utt- Δu+∫t0g(t-τ)Δudτ=|u|γu, where γ>0, and g is a nonnegative and decaying function. We prove a local existence theorem and show, for certain initial data and suitable conditions on g and γ, that this solution is global with energy which decays exponentially or polynomially depending on the rate of the decay of the relaxation function g.

AB - In a bounded domain, we consider utt- Δu+∫t0g(t-τ)Δudτ=|u|γu, where γ>0, and g is a nonnegative and decaying function. We prove a local existence theorem and show, for certain initial data and suitable conditions on g and γ, that this solution is global with energy which decays exponentially or polynomially depending on the rate of the decay of the relaxation function g.

KW - Exponential decay

KW - Global existence

KW - Local existence

KW - Nonlinear source

KW - Polynomial decay

KW - Relaxation function

KW - Viscoelastic

UR - http://www.scopus.com/inward/record.url?scp=33644895454&partnerID=8YFLogxK

U2 - 10.1016/j.na.2005.08.015

DO - 10.1016/j.na.2005.08.015

M3 - Article

AN - SCOPUS:33644895454

SN - 0362-546X

VL - 64

SP - 2314

EP - 2331

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 10

ER -

Existence and decay of solutions of a viscoelastic equation with a nonlinear source

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this