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Volume 8, Number 1, 2018, Pages 390-401                                                                DOI:10.11948/2018.390
General energy decay for a degenerate viscoelastic Petrovsky-type plate equation with boundary feedback
Fushan Li,Guangwei Du
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 \[ K(\mbox{\boldmath $x$})u_{tt}+\Delta^2u-\int_0^tg(t-s)\Delta^2u(s)ds+f(u)=0 \] 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.
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