Dynamical properties of second-order in time partial integro-differential equations: existence, regularity, and upper semicontinuity of pullback attractors

Abstract

In this work, we study dynamic properties, in the sense of pullback dynamics, for non- linear evolution processes of certain classes of dissipative semi-linear and non-autonomous

second-order integro-differential equations under suitable integrability conditions. More precisely, we consider the semilinear Cauchy problems associated with these equations, and we prove results on local and global well-posedness, existence of pullback attractors, regularity of pullback attractors, and upper semicontinuity of attractors with respect to variations in the functional parameters of the models over spaces of functions continuously embedded in fractional Sobolev spaces.