On the long-time behavior of the solution of a non linear viscoelastic plate equation with infinite memory and general kernel

In this paper, we investigate the asymptotic behavior of the solution of a nonlinear viscoelastic plate equation with infinite memory. The nonlinearity in this problem is of a logarithmic type. We use a minimal condition on a relaxation function h ∈ L¹(0, ∞); that is h^′ (t) ≤ −ξ(t)H(h(t)), where ξ is a nonincreasing function and H is an increasing and convex function near the origin. We establish an explicit energy decay formula under this very general assumption on the behavior of the relaxation function at infinity. Our results substantially improve some earlier results in the literature.