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The birth of a cusp in the two-dimensional, undercooled Stefan problem

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Herrero, Miguel A. y Medina Reus, Elena y Velázquez, J.J. L. (2000) The birth of a cusp in the two-dimensional, undercooled Stefan problem. Quarterly of Applied Mathematics, 58 (3). pp. 473-494. ISSN 0033-569X

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This paper deals with the one-phase, undercooled Stefan problem, in space dimension N = 2. We show herein that planar, one-dimensional blow-up behaviours corresponding to the undercooling parameter Delta = 1 are unstable with respect to small, transversal perturbations, The solutions thus produced are shown to generically generate crisps in finite time, when they exhibit an undercooling Delta = 1 - O(c) < 1, where 0 < c << 1, and epsilon is a parameter that measures the strength of the perturbation. The asymptotic behaviour of solutions and interfaces near their cusps is also obtained. All results are derived by means of matched asymptotic expansions techniques.


Tipo de documento:Artículo
Palabras clave:Stefan problem; undercooling; interfaces; asymptotic behaviour; matched asymptotic expansions
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:17887
Depositado:23 Ene 2013 11:15
Última Modificación:15 Abr 2015 07:24

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