Stackelberg–Nash null controllability for some linear and semilinear degenerate parabolic equations

Abstract

This paper deals with the application of Stackelberg–Nash strategies to the null controllability of degenerate parabolic equations. We assume that we can act on the system through a hierarchy of controls. A first control (the leader) is assumed to determine the policy; then, a Nash equilibrium pair (corresponding to a noncooperative multi-objective optimization strategy) is found; this governs the action of other controls (the followers). This way, the state of the system is driven to zero and, consequently, we solve a hierarchical null controllability problem. The main novelty in this paper is that the physical systems are governed by linear or semilinear 1D heat equations with degenerate coefficients.