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arXiv · 2503.11929

Local controllability of a free-boundary problem for a class of one-dimensional degenerate parabolic equations

Lingyang Liu
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Abstract

This paper is devoted to a study of the controllability of a free-boundary problem for a class of one-dimensional degenerate parabolic equations with distributed controls, locally supported in space. We prove that for any $T>0$, if the initial state is sufficiently small, there exists a control that drives the state exactly to rest at time $t = T$. The proof is based on Schauder's fixed point theorem, combined with appropriate estimates for solutions to degenerate parabolic equations and for control functions.

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Lingyang Liu. 2025-03-15. Local controllability of a free-boundary problem for a class of one-dimensional degenerate parabolic equations. https://arxiv.org/abs/2503.11929

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