Nonlinear damped wave equation: Existence and blow-up

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

doi:10.1016/j.camwa.2017.07.048

Nonlinear damped wave equation: Existence and blow-up

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

^*Corresponding author for this work

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

94 Scopus citations

Abstract

In this paper, we consider the following nonlinear wave equation with variable exponents: u_tt−Δu+au_t|u_t|^m(⋅)−2=bu|u|^p(⋅)−2,where a,b are positive constants. By using the Faedo–Galerkin method, the existence of a unique weak solution is established under suitable assumptions on the variable exponents m and p. We also prove the finite time blow-up of solutions and give a two-dimension numerical example to illustrate the blow up result.

Original language	English
Pages (from-to)	3024-3041
Number of pages	18
Journal	Computers and Mathematics with Applications
Volume	74
Issue number	12
DOIs	https://doi.org/10.1016/j.camwa.2017.07.048
State	Published - 15 Dec 2017

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Publisher Copyright:
© 2017 Elsevier Ltd

Keywords

Blow up
Existence
Nonlinear damping
Variable nonlinearity

ASJC Scopus subject areas

Modeling and Simulation
Computational Mathematics
Computational Theory and Mathematics

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10.1016/j.camwa.2017.07.048

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title = "Nonlinear damped wave equation: Existence and blow-up",

abstract = "In this paper, we consider the following nonlinear wave equation with variable exponents: utt−Δu+aut|ut|m(⋅)−2=bu|u|p(⋅)−2,where a,b are positive constants. By using the Faedo–Galerkin method, the existence of a unique weak solution is established under suitable assumptions on the variable exponents m and p. We also prove the finite time blow-up of solutions and give a two-dimension numerical example to illustrate the blow up result.",

keywords = "Blow up, Existence, Nonlinear damping, Variable nonlinearity",

author = "Messaoudi, \{Salim A.\} and Talahmeh, \{Ala A.\} and Al-Smail, \{Jamal H.\}",

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year = "2017",

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day = "15",

doi = "10.1016/j.camwa.2017.07.048",

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T1 - Nonlinear damped wave equation

T2 - Existence and blow-up

AU - Messaoudi, Salim A.

AU - Talahmeh, Ala A.

AU - Al-Smail, Jamal H.

PY - 2017/12/15

Y1 - 2017/12/15

N2 - In this paper, we consider the following nonlinear wave equation with variable exponents: utt−Δu+aut|ut|m(⋅)−2=bu|u|p(⋅)−2,where a,b are positive constants. By using the Faedo–Galerkin method, the existence of a unique weak solution is established under suitable assumptions on the variable exponents m and p. We also prove the finite time blow-up of solutions and give a two-dimension numerical example to illustrate the blow up result.

AB - In this paper, we consider the following nonlinear wave equation with variable exponents: utt−Δu+aut|ut|m(⋅)−2=bu|u|p(⋅)−2,where a,b are positive constants. By using the Faedo–Galerkin method, the existence of a unique weak solution is established under suitable assumptions on the variable exponents m and p. We also prove the finite time blow-up of solutions and give a two-dimension numerical example to illustrate the blow up result.

KW - Blow up

KW - Existence

KW - Nonlinear damping

KW - Variable nonlinearity

UR - https://www.scopus.com/pages/publications/85029477594

U2 - 10.1016/j.camwa.2017.07.048

DO - 10.1016/j.camwa.2017.07.048

M3 - Article

AN - SCOPUS:85029477594

SN - 0898-1221

VL - 74

SP - 3024

EP - 3041

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 12

ER -

Nonlinear damped wave equation: Existence and blow-up

Abstract

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Keywords

ASJC Scopus subject areas

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