Herrero, Miguel A.Velázquez, J.J. L.2023-06-202023-06-201996-040956-792510.1017/S0956792500002266https://hdl.handle.net/20.500.14352/58710It 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.journal articlehttp://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2320636http://journals.cambridge.orgmetadata only access517.9536.2Blowing-up solutionssupercooled Stefan problemoxygen diffusion-consumption problembehaviour of the free boundaryextinction pointEcuaciones diferenciales1202.07 Ecuaciones en Diferencias