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Herraiz, Luis A. and Herrero, Miguel A. and Velázquez, J.J. L.
(2001)
*A note on the dissolution of spherical crystals.*
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 131
(2).
pp. 371-389.
ISSN 0308-2105

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Official URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=1201356

## Abstract

We consider here the radial Stefan problem with Gibbs-Thomson law, which is a classical model describing growth or melting of a spherical crystal in a surrounding liquid. We shall specialize to the cases of two and three space dimensions and discuss the asymptotic behaviour of a melting crystal near its dissolution time t(*)>0. We prove here that, when the interface shrinks monotonically, the asymptotics near t=t(*) is of the form R(t)~(3σ(t(*)-t))(1/3), u(r,t)~-σ/r for r~R(t), r>R(t). Here, R(t) denotes the radius of the crystal, σ is a surface tension parameter and u(r,t) represents the field temperature. An important point to be noticed is that (*) exhibits no dependence on the space dimension N, in sharp contrast with results known for the case σ = 0.

Item Type: | Article |
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Uncontrolled Keywords: | Asymptotic behaviour; Stefan problem with Gibbs-Thomson law |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 17881 |

Deposited On: | 23 Jan 2013 08:56 |

Last Modified: | 12 Dec 2018 15:07 |

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