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This paper focuses on investigating the optimal actuator location forachieving minimum norm controls in the context of approximate controllabilityfor degenerate parabolic equations. We propose a formulation of theoptimization problem that encompasses both the actuator location and itsassociated minimum norm control. Specifically, we transform the problem into atwo-person zero-sum game problem, resulting in the development of fourequivalent formulations. Finally, we establish the crucial result that thesolution to the relaxed optimization problem serves as an optimal actuatorlocation for the classical problem.

Optimal Actuator Location of the Norm Optimal Controls for Degenerate Parabolic Equations