On the interaction between the viscoelasticity and the boundary variable-exponent nonlinearity in plate systems

Abstract

In this paper, we consider a viscoelastic plate system with a boundary frictional damping having a variable exponent $m(x)$. We investigate the competition between the two types of damping and their effects on the energy decay rates. Using the multiplier method, we establish explicit decay results depending on both m and the relaxation function g. Our results address both the optimality and generality and improve earlier related results in the literature.

Keywords:

• Plate equations
• energy decay rates
• frictional damping
• viscoelastic damping

2000 Mathematics Subject Classifications:

• 35B40
• 74D99
• 93D15
• 93D20

Disclosure statement

No potential conflict of interest was reported by the author(s).

 

Funding

This work was supported by MASEP Research Group in the Research Institute of Sciences and Engineering at University of Sharjah.

Data availability statement

My manuscript has no associated data.