Abstract
In this work, we are concerned with the null controllability of one-phase Stefan problems in star-shaped domains in \(\mathbb {R}^2\). We prove that, for fixed \(T>0\) and sufficient small initial data, there exist controls that drive the state to zero at time \(t=T\). Our approach relies on a null controllability result for parabolic systems in non-cylindrical domains, a complete analysis of the regularity of the controlled solution near the free boundary and a fixed-point argument.
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The first author was supported by CNPq - Brasil.
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Demarque, R., Fernández-Cara, E. Local null controllability of one-phase Stefan problems in 2D star-shaped domains. J. Evol. Equ. 18, 245–261 (2018). https://doi.org/10.1007/s00028-017-0399-x
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DOI: https://doi.org/10.1007/s00028-017-0399-x