General Decay for a Viscoelastic Equation of Variable Coefficients in the Presence of Past History with Delay Term in the Boundary Feedback and Acoustic Boundary Conditions

Acta Applicandae Mathematicae - Tập 154 - Trang 131-152 - 2017
Yamna Boukhatem1, Benyattou Benabderrahmane2
1Laboratory of Pure and Applied Mathematics, University of Laghouat, Laghouat, Algeria
2Laboratory of Pure and Applied Mathematics, Mohamed Boudiaf University, M’Sila, Algeria

Tóm tắt

In this paper, we consider a viscoelastic equation of variable coefficients in the presence of infinite memory (past history) with nonlinear damping term and nonlinear delay term in the boundary feedback and acoustic boundary conditions. Under suitable assumptions, two arbitrary decay results of the energy solution are established via suitable Lyapunov functionals and some properties of the convex functions. The first stability result is given with relation between the damping term and relaxation function. The second result is given without imposing any restrictive growth assumption on the damping term and the kernel function $g$ . Our result extends the decay result obtained for problems with finite history to those with infinite history.

Tài liệu tham khảo