Classical solutions of nonautonomous Riccati equations arising in parabolic boundary control problems (Q1288990)

The paper considers an abstract linear-quadratic regulator problem associated with linear parabolic systems in a bounded domain \(\Omega \subset R^n\) with boundary controls of Dirichlet or Neumann type. The solvability of the corresponding differential Riccati equation is obtained and a formal representation of the solution of this equation is given, which allows to obtain regularity results for boundary controls from \(L_2(\partial \Omega\times (0,T))\).