On Global Existence and Blow-Up of Solutions for an Integro-Differential Equation With Strong Damping

General decay of solutions of a viscoelastic equation

“…This blow-up result has been pushed to some situations, where the initial energy is positive, by Messaoudi [19]. A similar result has been also obtained by Wu [29] using a different method.…”

Exponential energy decay of solutions for a system of viscoelastic wave equations of Kirchhoff type with strong damping

“…Later, Rivera [12] showed the existence of global solutions for small datum and the total energy decays to zero exponentially under some restrictions. Then, Wu and Tsai [26] treated equation (1.2) for h(u t ) = −∆u t , they established the global existence as well as energy decay under assumption on the nonnegative kernel g ′ (t) ≤ −rg(t), ∀t ≥ 0 for some r > 0. This energy decay result was recently improved by Wu in [29] under a weaker condition on g (i.e., g ′ (t) ≤ 0 for t ≥ 0).…”

Global Well-Posedness for a Class of Kirchhoff-Type Wave System

“…Later, Munoz Rivera [4] showed the existence of global solutions for small initial value and the exponential decay of the total energy. Then Wu and Tsai [5] established the global existence and energy decay under the assumption ( ) ≤ − ( ), ℎ( ) = −Δ . Recently, this decay estimate was improved for a weaker condition on ( ) ≤ 0 in [6].…”