# Zero kinetic undercooling limit in the supercooled Stefan problem

@article{Baker2020ZeroKU, title={Zero kinetic undercooling limit in the supercooled Stefan problem}, author={Graeme Baker and Mykhaylo Shkolnikov}, journal={arXiv: Probability}, year={2020} }

We study the solutions of the one-phase supercooled Stefan problem with kinetic undercooling, which describes the freezing of a supercooled liquid, in one spatial dimension. Assuming that the initial temperature lies between the equilibrium freezing point and the characteristic invariant temperature throughout the liquid our main theorem shows that, as the kinetic undercooling parameter tends to zero, the free boundary converges to the (possibly irregular) free boundary in the supercooled… Expand

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McKean-Vlasov equations involving hitting times: blow-ups and global solvability

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- 2020

This paper is concerned with the analysis of blow-ups for two McKean-Vlasov equations involving hitting times. Let $(B(t); \, t \ge 0)$ be standard Brownian motion, and $\tau:= \inf\{t \ge 0: X(t)… Expand

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