Stability of Equilibria for the Stefan Problem With Surface Tension
نویسندگان
چکیده
منابع مشابه
Stability of Equilibria for the Stefan Problem With Surface Tension
We characterize the equilibrium states for the two-phase Stefan problem with surface tension and with or without kinetic undercooling, and we analyze their stability in dependence of physical and geometric quantities.
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Continuing our study of the Stefan problem with surface tension effect, in this paper, we establish sharp nonlinear stability and instability of steady circles. Our nonlinear stability proof relies on an energy method along the moving domain, and the discovery of a new ‘momentum conservation law’. Our nonlinear instability proof relies on a variational framework which leads to the sharp growth ...
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We develop a high-order energy method to prove asymptotic stability of flat steady surfaces for the Stefan problem with surface tension also known as the Stefan problem with Gibbs-Thomson correction.
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1. Introduction The classical Stefan problem is a model for phase transitions in solid-liquid systems and accounts for heat diiusion and exchange of latent heat in a homogeneous medium. The strong formulation of this model corresponds to a moving boundary problem involving a parabolic diiusion equation for each phase and a transmission condition prescribed at the interface separating the phases...
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The Stefan problem with small surface tension e is considered. Assuming that the classical Stefan problem (with s = 0) has a smooth free boundary T, we denote the temperature of the solution by 60 and consider an approximate solution 60 + su for the case where e ^ 0, e small. We first establish the existence and uniqueness of u , and then investigate the effect of u on the free boundary T. It i...
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ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2008
ISSN: 0036-1410,1095-7154
DOI: 10.1137/070700632