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

ABSTRACT: 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 (Hadži? & Shkoller 2014 Commun. Pure Appl. Math. 68, 689-757 (doi:10.1002/cpa.21522)) in which we studied nearly spherical shapes.

SUBMITTER: Hadzic M

PROVIDER: S-EPMC4535271 | biostudies-literature | 2015 Sep

REPOSITORIES: biostudies-literature

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

Hadžić Mahir M Shkoller Steve S

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 20150901 2050

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. M ...[more]

PMID: 26261359

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