Herrero, Miguel A.Medina Reus, ElenaVelázquez, J.J. L.2023-06-202023-06-202000-090033-569Xhttps://hdl.handle.net/20.500.14352/57837This 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.engjournal articlehttp://www.ams.org/publications/journals/journalsframework/qamhttp://www.ams.orgrestricted access517.956.4536.2Stefan problemundercoolinginterfacesasymptotic behaviourmatched asymptotic expansionsEcuaciones diferenciales1202.07 Ecuaciones en Diferencias