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

Abstract

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 $ 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, $ 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.

Keywords

• wave equation
• infinite memory
• distributed delay term
• viscoelastic term
• relaxation function