General decay of the solution energy in a viscoelastic equation with a nonlinear source

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

“…Proof of Theorem 2.2 From the ideas presented in [19][20][21][22][23], we get the following results. Multiplying (3.4) by ξ (t) and using (2.7) and (3.1), we get…”

“…Park [19] obtained the general decay estimates for a viscoelastic plate equation with time-varying delay under the condition (1.9). The stability of the solutions to a viscoelastic system under the condition (1.9) was studied in [20][21][22][23] and the references therein. With respect to wave equation with strong time delay, there is just little published work.…”

General Decay of Solutions of Nonlinear Viscoelastic Wave Equation

“…Then Messaoudi [7] improved these results by establishing a general decay of energy which is similar to the relaxation function.…”

“…By Lemma 3.1, (H1), we obtain Lemma 3.2. by using ξ(t) ≤ M . ( [7]) (Ω) and u 1 ∈ L 2 (Ω). If u is the solution of (1), then I(t) satisfies…”

Exponential energy decay and blow-up of solutions for a system of nonlinear viscoelastic wave equations with strong damping

“…This result has been extended by Messaoudi and Tatar [2,7] to the situation where g = 0 and exponential and polynomial decay results in the absence, as well as in the presence, of a source term have been established. Recently, Messaoudi [8,9] considered…”