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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 8
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Articles

Global existence and stability of a nonlinear wave equation with variable-exponent nonlinearities

Samah GhegalLaboratory of LEDPA, Mathematics Department, University of Batna 2, Batna, AlgeriaCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0003-0682-6789View further author information
ORCID Icon,
Ilhem HamchiLaboratory of LEDPA, Mathematics Department, University of Batna 2, Batna, AlgeriaView further author information
&
Salim A. MessaoudiDepartment of Mathematics and Statistics, KFUPM, Dhahran, Saudi ArabiaView further author information
Pages 1333-1343 | Received 30 Mar 2018, Accepted 23 Sep 2018, Published online: 12 Oct 2018
 
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ABSTRACT

In this paper, we consider a nonlinear wave equation with damping and source terms of variable-exponent types. First, we use the stable-set method to prove a global result. Then, by applying an integral inequality due to Komornik, we obtain the stability result.

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Acknowledgments

The authors thank an anonymous referee for his/her careful reading.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The third author is supported by KFUPM under Project No. FT 161004.

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