Our aim is to continue the study of abstract evolution equations in Banach spaces. A number of applications to partial differential equations of either parabolic, or hyperbolic, or Schroedinger type complemented with different kinds of boundary conditions will be given, allowing even the possibility that the domain of the solution varies in time. Such a study should lead to a posteriori error estimates for suitable approximation methods. Finally, we want to investigate the well-posedness of the Cauchy problem associated to doubly non linear opearator that are non local in time.
