General decay for a system of viscoelastic wave equation with past history, distributed delay and Balakrishnan-Taylor damping terms

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}_{+}\rightarrow {\bf R}_{+} $ holds true the below <disp-formula> <tex-math id=&qu...

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Published inElectronic research archive Vol. 30; no. 10; pp. 3902 - 3929
Main Authors Choucha, Abdelbaki, Boulaaras, Salah, Ouchenane, Djamel, Alkhalaf, Salem, Jan, Rashid
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
distributed delay term
infinite memory
relaxation function
viscoelastic term
wave equation
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Summary: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}_{+}\rightarrow {\bf R}_{+} $ holds true the below <disp-formula> <tex-math id="FE1"> \begin{document}$ g_{i}'(t)\leq-\zeta_{i}(t)G_{i}(g_{i}(t)), \quad \forall t\in {\bf R}_{+}, \quad {\rm{for}} \quad i = 1, 2, $\end{document} </tex-math></disp-formula> in which $ \zeta_{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.
ISSN:2688-1594
2688-1594
DOI:10.3934/era.2022199