General decay for a system of viscoelastic wave equation with past history, distributed delay and Balakrishnan-Taylor damping terms - Choucha, Abdelbaki; Boulaaras, Salah; Ouchenane, Djamel; Alkhalaf, Salem; Jan, Rashid (Electronic research archive, 2022)
The subject of this research is a coupled system of nonlinear viscoelastic wave equations with distributed delay components, infinite memory and Balakrishnan-Taylor damping. Assume the kernels $ g_{i} :{\bf R}_{+}→ {\bf R}_{+} $ holds true the below \begin{document}$ g_{i}'(t)≤-ζ_{i}(t)G_{i}(g_{i}(t)), \quad \forall t\in {\bf R}_{+}, \quad {\rm{for}} \quad i = 1, 2, $\end{document} in which $ ζ_{i} $ and $ G_{i} $ are functions. We demonstrate the stability of the system under this highly generic assumptions on the behaviour of $ g_i $ at infinity and by dropping the boundedness assumptions in the historical data.