On the general decay of a nonlinear viscoelastic plate equation with a strong damping and p⃗(x,t)-Laplacian

In this paper we consider a nonlinear viscoelastic plate equation with a lower order perturbation of a p⃗(x,t)-Laplacian operator of the formutt+Δ2u−Δp⃗(x,t)u+∫0tg(t−s)Δu(s)ds−ϵΔut+f(u)=0,(x,t)∈QT=Ω×(0,T), associated with initial and Dirichlet–Neumann boundary conditions.Under suitable conditions on gg,ff and the variable exponent of the p⃗(x,t)-Laplacian operator, we prove a general decay result in the presence of a strong damping ϵΔutϵΔut(ϵ>0)(ϵ>0) acting in the domain. This equation corresponds to a viscoelastic version arising in dynamics of elastoplastic flows and plate vibrations.