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Classical solutions of nonautonomous Riccati equations arising in parabolic boundary control problems. II. (English) Zbl 0952.49029
The authors consider an abstract linear-quadratic regulator problem associated with linear nonautonomous parabolic systems with boundary controls. The paper mostly is devoted to the proof of differentiability (with respect to the time parameters $$s$$, $$t$$) of the optimal state operator, which to a given initial value at a time $$s$$ assigns the optimal state at the time $$t$$.
[See also Part I in Appl. Math. Optimization 39, No. 3, 361-409 (1999; Zbl 0926.49019)].

##### MSC:
 49N10 Linear-quadratic optimal control problems 49K20 Optimality conditions for problems involving partial differential equations 49K27 Optimality conditions for problems in abstract spaces 35B37 PDE in connection with control problems (MSC2000)
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