Blow‐up and decay of solutions for a viscoelastic Kirchhoff‐type equation with distributed delay and variable exponents

Abstract

In this article, we focussed on a nonlinear viscoelastic Kirchhoff‐type equation with distributed delay and variable‐exponents. The blow‐up solutions of the problem are proved under suitable hypothesis, and by using an integral inequality due to Komornik, the general decay outcome is obtained in the case .

Blow-up of solutions for a system of nonlocal singular viscoelastic equations with sources and distributed delay terms

“…7 Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah, 64001, Iraq. 8…”

“…Recently, numerous authors have examined asymptotic behavior, stability, and blow-up phenomena of solutions in evolution systems with time delay. Refer to works by [6,8,9,19] for further details.…”