Stability in the Stefan Problem with Surface Tension (I)
نویسندگان
چکیده
منابع مشابه
Stability in the Stefan problem with surface tension (I)
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.
متن کاملStability in the Stefan problem with surface tension (II)
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 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.
متن کاملJ an 2 00 8 Stability in the Stefan problem with surface tension ( I )
The Stefan problem is one of the best known parabolic two-phase free boundary problems. It is a simple model of phase transitions in liquid-solid systems. Let Ω⊂Rn denote a domain that contains a liquid and a solid separated by an interface Γ. As the melting or cooling take place the boundary moves and we are naturally led to a free boundary problem. The unknowns are the temperatures of the liq...
متن کاملOn the Stefan Problem with Surface Tension
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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ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2010
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605300903405972