Global stability of steady states in the classical Stefan problem for general boundary shapes | Zendy

Mahir Hadžić | Zendy; Steve Shkoller | Zendy

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Global stability of steady states in the classical Stefan problem for general boundary shapes

Author(s) -

Mahir Hadžić,

Steve Shkoller

Publication year - 2015

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2014.0284

Subject(s) - stefan problem , convexity , mathematics , domain (mathematical analysis) , smoothness , a priori and a posteriori , stability (learning theory) , mathematical analysis , steady state (chemistry) , boundary (topology) , boundary value problem , computer science , philosophy , chemistry , epistemology , financial economics , economics , machine learning

The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady-state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of such steady states, assuming a sufficient degree of smoothness on the initial domain, but without any a priori restriction on the convexity properties of the initial shape. This is an extension of our previous result (Hadžić & Shkoller 2014 Commun. Pure Appl. Math. 68, 689-757 (doi:10.1002/cpa.21522)) in which we studied nearly spherical shapes.

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