Singularity formation in the one-dimensional supercooled Stefan problem
1996 ◽
Vol 7
(2)
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pp. 119-150
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Keyword(s):
Blow Up
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It is well-known that solutions to the one-dimensional supercooled Stefan problem (SSP) may exhibit blow-up in finite time. If we consider (SSP) in a half-line with zero flux conditions at t = 0, blow-up occurs if there exists T < ∞ such that limt↑Ts(t) > 0 and lim inft↑T⋅(t) = – ∞,s(t) being the interface of the problem under consideration. In this paper, we derive the asymptotics of solutions and interfaces near blow-up. We shall also use these results to discuss the possible continuation of solutions beyond blow-up.
2018 ◽
Vol 21
(4)
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pp. 901-918
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2009 ◽
Vol 20
(2)
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pp. 187-214
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1982 ◽
Vol 130
(1)
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pp. 385-398
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