Stackelberg-Nash strategy for the null controllability of semilinear degenerate equations in non-cylindrical domains

2025/09/30 by Gamboa, Alfredo S., Limaco, Juan, Yapu, Luis P.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.00173

Abstract

In this paper we use a Stackelberg-Nash strategy to show the local null controllability of a semilinear parabolic equation in one-dimension defined in a non-cylindrical domain where the diffusion coefficient degenerates at one point of the boundary. The linearized degenerated system is treated using a Carleman inequality for degenerated non-autonomous systems proved by the autors in [19] and the local controllability of the semilinear system is obtained using Liusterniks inverse function theorem.

Citations

• Hierarchical null controllability of a degenerate parabolic equation with nonlocal coefficient
• Controllability of a system of non-autonomous degenerate coupled parabolic equations
• Hierarchical exact controllability of the fourth order parabolic equations
• Hierarchical null controllability of a semilinear degenerate parabolic equation with a gradient term
• Null controllability for a degenerate population model in divergence form via Carleman estimates
• Carleman estimates and null controllability for a degenerate population model

Related

• Hierarchical null controllability of a degenerate parabolic equation with nonlocal coefficient
• Hierarchical null controllability of a semilinear degenerate parabolic equation with a gradient term
• Controllability of a system of non-autonomous degenerate coupled parabolic equations
• Hierarchical control for the semilinear parabolic equations with interior degeneracy
• Boundary null controllability of a class of 2-d degenerate parabolic PDEs