General decay for viscoelastic plate equation with p-Laplacian and time-varying delay

Abstract

In this paper we study the viscoelastic plate equation with p-Laplacian and time-varying delay. We establish a general decay rate result under some restrictions on the coefficients of strong damping and strong time-varying delay and weakening the usual assumptions on the relaxation function, using the energy perturbation method.MSC: 35B35; 37B25; 74Dxx; 93D20

Blow‐up results for a viscoelastic beam equation of p‐Laplacian type with strong damping and logarithmic source

“…by introducing suitable Lyapunov functionals, the authors established general estimates of decay of the associated energy, dependent on the behavior of both 𝜎 and g. When the equation is subjected to the action of a strong time-varying delay, Kang 31 obtained a general decay rate for the IBVP associated with the equation…”

“…When the equation is subjected to the action of a strong time‐varying delay, Kang 31 obtained a general decay rate for the IBVP associated with the equation $$$$ {u}_{tt}+\alpha {\Delta}^2u-{\Delta}_pu-{\int}_{-\infty}^tg\left(t-s\right){\Delta}^2u(s) ds-{\mu}_1\Delta {u}_t-{\mu}_2\Delta {u}_t\left(t-\tau (t)\right)=f(u)+h(x). $$$$ The same model without the influence of the $$$ p $$$‐Laplacian was addressed by Enyi et al 32 …”

Optimal decay for second‐order abstract viscoelastic equation in Hilbert spaces with infinite memory and time delay

“…where G is an increasing positive strictly convex function satisfying some additional properties. For the general decay results in the case of constant or varying time delay, see previous works [28][29][30][31][32][33][34] and references therein. In this work, we are interested in giving an optimal explicit and a general decay rates of the solution of the problem (1) under some assumptions on the function h, 1 and the weight of delay 2 .…”

“…They established a general decay results where the kernel memory satisfies Equation () and where G is an increasing positive strictly convex function satisfying some additional properties. For the general decay results in the case of constant or varying time delay, see previous works 28‐34 and references therein.…”