Well-posedness and stability of nonautonomous past systems with unbounded operators in the delay term

We study partial functional differential equations with nonautonomous past, in which we allow unbounded operators to act on the modified delay term. Using semigroup methods and perturbation theory on a product space, the well-posedness and the uniform exponential stability of the solutions are investigated. As an application, we treat a reaction-diffusion problem and we give a systematic treatment of second order Cauchy problems.