{"ID":2867355,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.19505","arxiv_id":"2509.19505","title":"Hierarchical null controllability of a degenerate parabolic equation with nonlocal coefficient","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, Límaco 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.","short_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...","url_abs":"https://arxiv.org/abs/2509.19505","url_pdf":"https://arxiv.org/pdf/2509.19505v1","authors":"[\"Juan Límaco\",\"João Carlos Barreira\",\"Suerlan Silva\",\"Luis P. Yapu\"]","published":"2025-09-23T19:23:14Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.AP\"]","methods":"[\"Diffusion Model\"]","has_code":false}