Premium
Global Stability and Decay for the Classical Stefan Problem
Author(s) -
Hadžić Mahir,
Shkoller Steve
Publication year - 2015
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21522
Subject(s) - stefan problem , mathematics , stability (learning theory) , a priori and a posteriori , domain (mathematical analysis) , boundary (topology) , homogeneous , phase transition , distribution (mathematics) , heat equation , mathematical analysis , derivative (finance) , free boundary problem , thermodynamics , physics , computer science , financial economics , economics , philosophy , epistemology , combinatorics , machine learning
The classical one‐phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition, such as ice melting to water. This is accomplished by solving the heat equation on a time‐dependent domain whose boundary is transported by the normal derivative of the temperature along the evolving and a priori unknown free boundary. We establish a global‐in‐time stability result for nearly spherical geometries and small temperatures, using a novel hybrid methodology, which combines energy estimates, decay estimates, and Hopf‐type inequalities.© 2015 Wiley Periodicals, Inc.