Asymptotic Behavior of a Class of Abstract Semilinear Integrodifferential Equations and Applications

A class of semilinear hyperbolic Volterra integrodifferential equations in Hilbert spaces is considered. The main results in this paper are the global existence of solutions to the initial problem of the equation for large data and an asymptotic estimation of the solution. An application to a system relating to three-dimensional viscoelastic dynamics is presented