Plate equations with frictional and viscoelastic dampings

Abstract

In this paper, we consider the plate equation with both weak frictional damping and viscoelastic damping acting simultaneously and complementarily in the domain. An energy decay rate formula is obtained under nonrestrictive hypotheses on the relaxation function and the frictional damping term. Our results improve and generalize previous results existing in the literature.

Keywords:

• Plate equation
• general decay
• weak frictional damping
• viscoelasticity

AMS Subject Classifications:

• 35B37
• 35L55
• 74D05
• 93D15
• 93d20

Acknowledgements

The authors thank the University of Sharjah and King Fahd University of Petroleum and Minerals for their continuous support.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by University of Sharjah and King Fahd University of Petroleum and Minerals.