Well-posedness and asymptotic stability results for a viscoelastic plate equation with a logarithmic nonlinearity

ABSTRACT

In this paper, we consider a viscoelastic plate equation with a velocity-dependent material density and a logarithmic nonlinearity. Using the Faedo-Galaerkin approximations and the multiplier method, we establish the existence of the solutions of the problem and we prove an explicit and general decay rate result. These results extend and improve many results in the literature.

KEYWORDS:

• Asymptotic stability
• viscoelastic
• plate equation
• logarithmic nonlinearity

AMS SUBJECT CLASSIFICATIONS:

• 35B35
• 35L55
• 75D05
• 74D10
• 93D20

Acknowledgements

The authors thank KFUPM for its continuous support.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was funded by King Fahd University of Petroleum and Minerals (KFUPM) under Project #IN151023. This work was initiated during the visit of the second author to KFUPM in December 2016.