Memory Effects on the Stability of Viscoelastic Timoshenko Systems in the Whole 1D-Space

Abstract

In this paper, we investigate new classes of viscoelastic Timoshenko-Ehrenfest systems under the presence of full or partial memory effects. Our achievements rely on recent approaches to the theory of dissipative structure for systems of differential equations, by featuring optimal pointwise estimates in the Fourier space, L ²-estimates for the solutions, and explicit energy decay rates depending on the viscoelastic damping coupling. Therefore, under a complete stability analysis, original results as well as improvements of previous work in the literature are our main findings.