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- Title
On melting and freezing for the 2D radial Stefan problem.
- Authors
Hadžić, Mahir; Raphaël, Pierre
- Abstract
We consider the two-dimensional free boundary Stefan problem describing the evolution of a spherically symmetric ice ball {r ≤ λ(t)}. We revisit the pioneering analysis of [31] and prove the existence in the radial class of finite time melting regimes... which respectively correspond to the fundamental stable melting rate, and a sequence of codimension k excited regimes. Our analysis fully revisits a related construction for the harmonic heat flow in [60] by introducing a new and canonical functional framework for the study of type II (i.e. nonself-similar) blow-up. We also show a deep duality between the construction of the melting regimes and the derivation of a discrete sequence of global-in-time freezing regimes... which correspond respectively to the fundamental stable freezing rate, and excited regimes which are codimension k stable.
- Subjects
MATHEMATICAL singularities; DERIVATIVES (Mathematics); DIRICHLET problem; PHASE transitions; CAUCHY problem
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2019, Vol 21, Issue 11, p3259
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/904