Nonautonomous Retarded Wave Equations

In this work we study the well-posedness of a class of retarded integrodifferential Volterra equations. The proofs are based on the nonautonomous version of Desch- Schappacher’s perturbation result and extrapolation theory. As an application, we get C2 solutions of the nonautonomous retarded wave equation with memory effects wtt t x = wxx t x + α x wx t x + 0 −r k1 t θ x wxx t + θ x dθ + 0 −r k2 t θ x wx t + θ x dθ + f t x 0 ≤ t x ∈ 0 l with Dirichlet boundary conditions