Decay Result for a Delay Viscoelastic Plate Equation

Abstract

In this work, we consider a fourth-order plate equation that represents the downward displacement of suspension bridge in the presence of viscoelastic and delay damping. We establish an optimal and general decay estimates with partially hinged boundary conditions under suitable assumptions on the relaxation function. This result improves and generalizes earlier results in the literature such as Kirane and Said-Houari (Z Angew Math Phys 62:1065–1082, 2011) and Zhifeng (Z Angew Math Phys 66:727–745, 2015).