Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2015; 52(3): 907-914

Printed May 31, 2015

https://doi.org/10.4134/BKMS.2015.52.3.907

Copyright © The Korean Mathematical Society.

Stability for a viscoelastic plate equation with $p$-Laplacian

Sun Hye Park

Pusan National University

Abstract

In this paper, we consider a viscoelastic plate equation with $p$-Laplacian $$ u'' + \Delta^2 u - div(|\nabla u|^{p-2} \nabla u) + \sigma(t) \int^t_0 g(t-s) \Delta u(s) ds - \Delta u' = 0 .$$ By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of both $\sigma$ and $g$.

Keywords: plate equation, $p$-laplacian, weak viscoelasticity, general decay

MSC numbers: 35L70, 35B40

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