2026-06-28T04:48:18Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/578372023-08-11T09:15:37Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Herrero, Miguel A.
author
Medina Reus, Elena
author
Velázquez, J.J. L.
2023-06-20T17:08:38Z
2023-06-20T17:08:38Z
2000-09
0033-569X
https://hdl.handle.net/20.500.14352/57837
http://www.ams.org/publications/journals/journalsframework/qam
http://www.ams.org
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.
eng
The birth of a cusp in the two-dimensional, undercooled Stefan problem
journal article
URL
https://docta.ucm.es/bitstreams/62cb6455-d55f-4814-ad1d-0cbb5fce4ed4/download
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1874a6d103af514c629da403d1f7622e
311912
application/pdf
Herrero24.pdf
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https://docta.ucm.es/bitstreams/5a2323b7-f656-4323-9d9c-978f5799dc17/download
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1b70f87af6fdb6f73d267b35669fa6d4
24
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Herrero24.pdf.txt