Distributed optimal control of lambda–omega systems

Abstract

The formulation, analysis, and numerical solution of distributed optimal control problems governed by lambda–omega systems is presented. These systems provide a universal model for reaction-diffusion phenomena with turbulent behavior. Existence and regularity properties of solutions to the free and controlled lambda–omega models are investigated. To validate the ability of distributed control to drive lambda–omega systems from a chaotic to an ordered state, a space-time multigrid method is developed based on a new smoothing scheme. Convergence properties of the multigrid scheme are discussed and results of numerical experiments are reported.