具有表面张力的相容Stefan问题解的定性行为
Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension
摘要：
研究了具有表面张力和有无动力学过冷的两相Stefan问题的定性行为。结果表明，这些问题产生的局部半流定义良好的状态流形。如果一个解在下面精确的意义上不表现出奇点，则证明它在时间上全局存在，并且它的轨道是相对紧的。此外，还研究了平衡点的稳定性和不稳定性。特别是，它示出了相同半径的多个球体是不稳定的，让人想起奥斯特瓦尔德熟化的发病。
英文摘要：
The qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling is studied. 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 below, it is proved that it exists globally in time and its orbit is relatively compact. In addition, stability and instability of equilibria is studied. In particular, it is shown that multiple spheres of the same radius are unstable, reminiscent of the onset of Ostwald ripening.
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