Asymptotic behavior for a viscoelastic Kirchhoff equation with distributed delay and Balakrishnan–Taylor damping

Abstract

A nonlinear viscoelastic Kirchhoff-type equation with Balakrishnan–Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.

Growth and blow-up of solutions with positive initial energy for a viscoelastic Kirchhoff equation with a logarithmic nonlinearity, delay and Balakrishnan-Taylor damping terms

“…Here, the memory term's kernel function is denoted by ℶ. See ( [8], [13], [15], [20], [21], [22], [29]).…”

“…Recently, numerous authors have investigated the stability and asymptotic behavior of evolution systems with time delay. For further exploration, refer to works by ( [9], [10], [13]- [15], [18], [22], [32]).…”