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arXiv · 2509.19505

Hierarchical null controllability of a degenerate parabolic equation with nonlocal coefficient

Juan Límaco·João Carlos Barreira·Suerlan Silva·Luis P. Yapu
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Abstract

In this paper we use a Stackelberg-Nash strategy to show the local null controllability of a parabolic equation where the diffusion coefficient is the product of a degenerate function in space and a nonlocal term. We consider one control called \textit{leader} and two controls called \textit{followers}. To each leader we associate a Nash equilibrium corresponding to a bi-objective optimal control problem; then, we find a leader that solves the null controllability problem. The linearized degenerated system is treated adapting Carleman estimates for degenerated systems from Demarque, L\'imaco and Viana \cite{DemarqueLimacoViana_deg_sys2020} and the local controllability of the non-linear system is obtained using Liusternik's inverse function theorem. The nonlocal coefficient originates a multiplicative coupling in the optimality system that gives rise to interesting calculations in the applications of the inverse function theorem.

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Juan Límaco, João Carlos Barreira, Suerlan Silva, Luis P. Yapu. 2025-09-23. Hierarchical null controllability of a degenerate parabolic equation with nonlocal coefficient. https://arxiv.org/abs/2509.19505

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