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Singularity formation in the one-dimensional supercooled Stefan problem

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Herrero, Miguel A. and Velázquez, J.J. L. (1996) Singularity formation in the one-dimensional supercooled Stefan problem. European Journal of Applied Mathematics, 7 (2). pp. 119-150. ISSN 0956-7925

Official URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2320636


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Abstract

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↑T s(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.


Item Type:Article
Uncontrolled Keywords:Blowing-up solutions; supercooled Stefan problem; oxygen diffusion-consumption problem; behaviour of the free boundary; extinction point
Subjects:Sciences > Mathematics > Differential equations
ID Code:22659
Deposited On:27 Aug 2013 07:55
Last Modified:12 Dec 2018 15:08

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