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

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.

COMMUNICATED BY:

• Scott Hansen

KEYWORDS:

• Source term
• dissipative term
• variable exponents
• global solution
• stability

AMS SUBJECT CLASSIFICATIONS:

• 35L05
• 35B40
• 35L70
• 93D20

Acknowledgments

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

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Samah Ghegal  http://orcid.org/0000-0003-0682-6789

Additional information

Funding

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