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An abstract framework guaranteeing the local continuous differentiability ofthe value function associated with optimal stabilization problems subject toabstract semilinear parabolic equations subject to a norm constraint on thecontrols is established. It guarantees that the value function satisfies theassociated Hamilton-Jacobi-Bellman equation in the classical sense. Theapplicability of the developed framework is demonstrated for specificsemilinear parabolic equations.

applied mathematics and optimization/applied mathematics and optimization

Differentiability of the Value Function of Semilinear Parabolic Infinite  Time Horizon Optimal Control Problems on $L^2(\Omega)$ under Control  Constraints