Identification of operators in systems governed by evolution equations on Banach space

Optimal Control Problems for Nonlinear Hyperbolic Distributed Parameter Systems with Damping Terms

“…Using the system and adjoint system equations, the necessary optimality conditions are completely characterized. These conditions extend the former results in [10,2,3,13] to two directions, one is nonlinear equations and the other is damped equations.…”

“…The related optimal control and parameter estimation problems for linear systems, i.e., f ðt; yÞ ¼ f ðtÞ, are studied extensively by Ahmed [1,2], Banks et al [5,6] and Omatsu and Seinfeld [13] in the framework of Gelfand triple or fivefold. We also intend to extend some of their results to our nonlinear system.…”

Minimax control of nonlinear evolution equations

“…Similar problems for different classes of systems were recently considered by Ahmed [17], [18] and Tanimoto [19]. The reader can consult them and the references therein for further details and different aspects of the problem.…”

Optimal Control Problems for Parabolic Hemivariational Inequalities With Boundary Conditions

“…is compact in view of Theorem 2 of Aubin [1]. Hence, the mapping u → x is compact from L 2 (0, T ; U ) to L 2 (0, T ; H).…”

“…In Section 2 we study the regularity and a variational of constant formula for solutions of parabolic hemivariational inequality. The existence and regularity for the nondegenerate nonlinear systems has been developed as seen in Theorem 4.1 of [1] or Theorem 2.6 of [3], and the references therein. Thereafter, in Section 3, we prove the existence and the uniqueness of optimal control for the problem (1.1).…”