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