Semigroups and linear partial differential equations with delay
  We prove the equivalence of the well-posedness of a partial differential equation with delay and an associated abstract Cauchy problem. This is used to derive sufficient conditions for well-posedness, exponential stability and norm continuity of the solutions. Applications to a reaction-diffusion equation with delay are given. 
Andr\'as B\'atkai and Susanna Piazzera
math.FA math.DS