Well-posedness and optimal decay rates for the viscoelastic Kirchhoff equation

Abstract

In this paper, we investigate the well-posedness as well as optimal decay rate estimates of the energy associated with a Kirchhoff-Carrier problem in n-dimensional bounded domain under an internal finite memory. The considered class of memory kernels is very wide and allows us to derive new and optimal decay rate estimates then those ones considered previously in the literature for Kirchhoff-type models.