English

On thermodynamically consistent Stefan problems with variable surface energy

Analysis of PDEs 2016-12-20 v2

Abstract

A thermodynamically consistent two-phase Stefan problem with temperature-dependent 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, it is proved that it exists globally in time and converges towards an equilibrium of the problem. In addition, stability and instability of equilibria is studied. In particular, it is shown that multiple spheres of the same radius are unstable if surface heat capacity is small; however, if kinetic undercooling is absent, they are stable if surface heat capacity is sufficiently large.

Keywords

Cite

@article{arxiv.1109.4542,
  title  = {On thermodynamically consistent Stefan problems with variable surface energy},
  author = {Jan Pruess and Gieri Simonett and Mathias Wilke},
  journal= {arXiv preprint arXiv:1109.4542},
  year   = {2016}
}

Comments

To appear in Arch. Ration. Mech. Anal. The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-015-0938-y. arXiv admin note: substantial text overlap with arXiv:1101.3763

R2 v1 2026-06-21T19:08:14.911Z