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

Abstract

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.

56 pages. Expanded introduction, added references. This revised version is published in Arch. Ration. Mech. Anal. (207) (2013), 611-667

References in corpus (4)

• Orthogonality conditions and asymptotic stability in the Stefan problem with surface tension
• On thermodynamically consistent Stefan problems with variable surface energy
• Darcy's flow with prescribed contact angle -- Well-posedness and lubrication approximation
• Maximal regularity with temporal weights for parabolic problems with inhomogeneous boundary conditions

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