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Many physical systems are modeled by nonlinear parabolic differentialequations, such as the Kuramoto-Sivashinsky (KS) equation. In this paper, theexistence of a concurrent optimal controller and actuator design is establishedfor semilinear parabolic systems. Optimality equations are provided. Theresults are shown to apply to optimal controller/actuator design for theKuramoto-Sivashinsky equation and also nonlinear diffusion.

Optimal Controller and Actuator Design for Nonlinear Parabolic Systems