Hadžić, M;
Raphaël, P;
(2019)
On melting and freezing for the 2D radial Stefan problem.
Journal of the European Mathematical Society
, 21
(11)
pp. 3259-3341.
10.4171/jems/904.
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Abstract
We consider the two dimensional free boundary Stefan problem describing the evolution of a spherically symmetric ice ball {r≤λ(t)}. We revisit the pioneering analysis of [31] and prove the existence in the radial class of finite time melting regimes λ(t)=⎧⎩⎨⎪⎪⎪⎪⎪⎪(T−t)1/2e−2√2|ln(T−t)|√+O(1)(c+o(1))(T−t)k+12|ln(T−t)|k+12k, k∈N∗ as t→T which respectively correspond to the fundamental stable melting rate, and a sequence of codimension k excited regimes. Our analysis fully revisits a related construction for the harmonic heat flow in [60] by introducing a new and canonical functional framework for the study of type II (i.e. non-self-similar) blow up. We also show a deep duality between the construction of the melting regimes and the derivation of a discrete sequence of global-in-time freezing regimes λ∞−λ(t)∼⎧⎩⎨1logt1tk(logt)2, k∈N∗ as t→+∞ which correspond respectively to the fundamental stable freezing rate, and excited regimes which are codimension k stable
Type: | Article |
---|---|
Title: | On melting and freezing for the 2D radial Stefan problem |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.4171/jems/904 |
Publisher version: | https://doi.org/10.4171/jems/904 |
Language: | English |
Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
Keywords: | Stefan problem, finite time melting, singularity formation |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10088044 |
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