Nonautonomous retarded wave equations

In this work we study the well-posedness of a class of retarded integrodiff erential Volterra equations. The proofs are based on the nonautonomous vers ion of Desch-Schappacher's perturbation result and extrapolation theory. As an application, we get C-2 solutions of the nonautonomous retarded wave eq uation with memory effects w(tt)(t,x) = w(xx) (t,x) + alpha (x)w(x) (t,x) + integral (0)(-r)(t, theta, x)w(xx)(t + theta, x)d theta + integral (0)(-r)k(2)(t, theta, x)w(x)(t + theta, x)d theta + f(t,x), 0 le ss than or equal to t, x is an element of [0, l], with Dirichlet boundary Conditions. (C) 2001 Academic Press.