Asymptotic behavior of solutions of a viscoelastic Shear beam model with no rotary inertia: General and optimal decay results

In this study, we consider a viscoelastic Shear beam model with no rotary inertia. Specifically, we study - + + * = - + + =. f. f. g f t b.. f. 0, 0,tt x x xx xx x1 () ()() () where the convolution memory function g belongs to a class of L1 0, 8 () functions that satisfies g'( t) = -.(t).(g(t)),. t = 0, where. is a positive nonincreasing differentiable function and. is an increasing and convex function near the origin. Using just this general assumptions on the behavior of g at infinity, we provide optimal and explicit general energy decay rates from which we recover the exponential and polynomial rates when.(s) = sp and p covers the full admissible range [1, 2). Given this degree of generality, our results improve some of earlier related results in the literature.