Decay for solutions of a nonlinear damped wave equation with variable-exponent nonlinearities

Salim A. Messaoudi; Jamal H. Al-Smail; Ala A. Talahmeh

doi:10.1016/j.camwa.2018.07.035

Decay for solutions of a nonlinear damped wave equation with variable-exponent nonlinearities

Salim A. Messaoudi^*, Jamal H. Al-Smail, Ala A. Talahmeh

^*Corresponding author for this work

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

39 Scopus citations

Abstract

In this paper, we consider the following nonlinear waveequation with variable exponents: u_tt−div(|∇u|^r(⋅)−2∇u)+|u_t|^m(⋅)−2u_t=0.By using a lemma by Komornik, we prove the decay estimates for the solution under suitable assumptions on the variable exponents m,r and the initial data. We also give two numerical applications to illustrate our theoretical results.

Original language	English
Pages (from-to)	1863-1875
Number of pages	13
Journal	Computers and Mathematics with Applications
Volume	76
Issue number	8
DOIs	https://doi.org/10.1016/j.camwa.2018.07.035
State	Published - 15 Oct 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Ltd

Keywords

Decay
Variable exponent
Wave equation

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.camwa.2018.07.035

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title = "Decay for solutions of a nonlinear damped wave equation with variable-exponent nonlinearities",

abstract = "In this paper, we consider the following nonlinear waveequation with variable exponents: utt−div(|∇u|r(⋅)−2∇u)+|ut|m(⋅)−2ut=0.By using a lemma by Komornik, we prove the decay estimates for the solution under suitable assumptions on the variable exponents m,r and the initial data. We also give two numerical applications to illustrate our theoretical results.",

keywords = "Decay, Variable exponent, Wave equation",

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AU - Messaoudi, Salim A.

AU - Al-Smail, Jamal H.

AU - Talahmeh, Ala A.

PY - 2018/10/15

Y1 - 2018/10/15

N2 - In this paper, we consider the following nonlinear waveequation with variable exponents: utt−div(|∇u|r(⋅)−2∇u)+|ut|m(⋅)−2ut=0.By using a lemma by Komornik, we prove the decay estimates for the solution under suitable assumptions on the variable exponents m,r and the initial data. We also give two numerical applications to illustrate our theoretical results.

AB - In this paper, we consider the following nonlinear waveequation with variable exponents: utt−div(|∇u|r(⋅)−2∇u)+|ut|m(⋅)−2ut=0.By using a lemma by Komornik, we prove the decay estimates for the solution under suitable assumptions on the variable exponents m,r and the initial data. We also give two numerical applications to illustrate our theoretical results.

KW - Decay

KW - Variable exponent

KW - Wave equation

UR - https://www.scopus.com/pages/publications/85051086420

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DO - 10.1016/j.camwa.2018.07.035

M3 - Article

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JF - Computers and Mathematics with Applications

IS - 8

ER -

Decay for solutions of a nonlinear damped wave equation with variable-exponent nonlinearities

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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