Classical solutions of nonautonomous Riccati equations arising in parabolic boundary control problems

An abstract linear-quadratic regulator problem over finite time horizon is considered; it covers a large class of linear nonautonomous parabolic syste ms in bounded domains, with boundary control of Dirichlet or Neumann type. The associated differential Riccati equation is studied from the point of v iew of semigroup theory; it is shown to have a classical, explicitly repres ented solution for very general final data; weighted Holder regularity resu lts for the optimal pair are deduced.