Local existence and blow up of solutions to a logarithmic nonlinear wave equation with delay

ABSTRACT

This paper is concerned with a problem of a logarithmic nonlinear wave equation with delay. The local existence result has been established using the semigroup theory. In addition, for negative initial energy, a finite-time blow-up result is proved.

COMMUNICATED BY:

• Scott Hansen

KEYWORDS:

• Logarithmic source
• blow up
• wave equation
• negative initial energy
• delay

AMS CLASSIFICATIONS:

• 35B05
• 35L05
• 35L15
• 35L70

Acknowledgements

The authors would like to express their sincere thanks to King Fahd University of Petroleum and Minerals for its support.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been funded by King Fahd University of Petroleum and Minerals (KFUPM) under Project # IN151006.