Qualitative Behavior of Solutions for Thermodynamically Consistent Stefan Problems with Surface Tension

  title={Qualitative Behavior of Solutions for Thermodynamically Consistent Stefan Problems with Surface Tension},
  author={Jan Pr{\"u}ss and Gieri Simonett and Rico Zacher},
We study the qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling. It is shown that these problems generate local semiflows in well-defined state manifolds. If a solution does not exhibit singularities in a sense made precise herein, it is proved that it exists globally in time and its orbit is relatively compact. In addition, stability and instability of equilibria are studied. In particular, it is shown… CONTINUE READING
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