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

摘要

In this paper, we consider a viscoelastic plate equation with $p$-Laplacian $$ u'' + Delta^2 u - div(|abla u|^{p-2} abla u) + sigma(t) int^t_0 g(t-s) Delta u(s) ds - Delta u' = 0 .$$ 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 $g$.