Infinite-horizon linear-quadratic regulator problems for nonautonomous parabolic systems with boundary control

This paper concerns the classical linear-quadratic regulator problem for general nonautonomous parabolic systems with boundary control over infinite time horizon from the point of view of semigroup theory. Under appropriate assumptions we prove existence and uniqueness of the optimal pair, as well as existence, uniqueness, and further properties of the solution of the associated Riccati equation. Several examples are discussed in detail.