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General energy decay for a degenerate viscoelastic Petrovsky-type plate equation with boundary feedback
Keywords:General energy decay, Degenerate Petrovsky plate equation, Boundary feedback, Function approximation
Abstract:
      In this paper, we consider a degenerate viscoelastic Petrovsky-type plate equation \begin{align*} K(\mbox{\boldmath $x$})u_{tt}+\Delta^2u-\int_0^tg(t-s)\Delta^2u(s)ds+f(u)=0 \end{align*} with boundary feedback. Under the weaker assumption on the relaxation function, the general energy decay is proved by priori estimates and analysis of Lyapunov-like functional. The exponential decay result and polynomial decay result in some literature are special cases of this paper.