Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension

Details Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension

2011-01-19

arxiv.org/abs/1101.3763v1

Mathematics

Analysis of PDEs

48 pages

Scientific paper

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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