Local controllability of free boundary three-dimensional semilinear radial parabolic equations

2025/11/13 by Límaco, Juan, Yapu, Luis P.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.10795

Abstract

We prove that a free boundary semilinear heat equation with Stefan boundary condition and radially symmetric data is locally null controllable. The strategy involves reducing the problem to the corresponding one-dimensional formulation and adapting a Carleman inequality in that setting. The local null controllability of the free-boundary problem is then established via the Schauder fixed-point theorem. To the best of our knowledge, this is the first controllability result for this problem with Stefan boundary condition in more than one spatial dimension.

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