A blow-up result for a nonlinear wave equation with variable-exponent nonlinearities

Abstract

In this paper, we consider the following wave equation:

in which is a nonnegative constant and the exponents of nonlinearity are given functions. For arbitrary positive initial energy, we prove a finite-time blow-up result.

Keywords:

• Blow up
• nonlinear wave equation
• Sobolev spaces with variable exponents
• variable nonlinearity

AMS Subject Classifications:

• 35B44
• 35D30
• 35L70

Acknowledgements

The authors thank King Fahd University of Petroleum and Minerals for its support. This work is sponsored by KFUPM under Project No. SF161-Math-84.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is sponsored by KFUPM under [Project Number SF161-Math-84].