Generalizations of the Stefan Problem

  • Augusto Visintin
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 28)


Two features that determine the onset of undercooling and superheating in phase transitions are studied here:
  1. (i)

    Nonequilibrium at solid-liquid interfaces. Here this is described by so-called phase relaxation, which also provides a model for glass formation.

  2. (ii)

    Nonhomogeneity, that is, the presence of a second chemical component. This is described at first by coupling the equations of thermal and material diffusion, and then in the framework of the theory of nonequilibrium thermodynamics. The latter approach is also outlined in a more general setting, including the presence of several components and chemical reactions.


These problems can be treated by applying results and techniques of Chaps. II and III.

The general role of free energy in thermodynamical evolution is briefly examined on the basis of the second principle.


Phase Transition Free Boundary Problem Stefan Problem Phase Relaxation Nonequilibrium Thermodynamic 
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© Birkhäuser Boston 1996

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  • Augusto Visintin

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