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math.AP2021★ 20 cited
On behavior of solutions to a Petrovsky equation with damping and variable-exponent source
Menglan Liao, Zhong Tan
This paper deals with the following Petrovsky equation with damping and nonlinear source \[u_{tt}+Δ^2 u-M(\|\nabla u\|_2^2)Δu-Δu_t+|u_t|^{m(x)-2}u_t=|u|^{p(x)-2}u\] under initial-b…
math.AP2021
Asymptotic stability for a class of viscoelastic equations with general relaxation functions and the time delay
Menglan Liao, Zhong Tan
The goal of the present paper is to study the viscoelastic wave equation with the time delay \[ |u_t|^ρu_{tt}-Δu-Δu_{tt}+\int_0^tg(t-s)Δu(s)ds+μ_1u_t(x,t)+μ_2 u_t(x,t-τ)=b|u|^{p-2}…