Gunduz Caginalp1, Xinfu Chen1
1Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
Tóm tắt
We consider the distinguished limits of the phase field
equations and prove that the corresponding free boundary problem is
attained in each case. These include the classical Stefan
model, the surface tension model (with or without kinetics), the surface
tension model with
zero specific heat, the two phase Hele–Shaw, or quasi-static,
model. The Hele–Shaw model is
also a limit of the Cahn–Hilliard equation, which is itself
a limit of the phase field equations.
Also included in the distinguished limits is the motion by mean
curvature model that is a limit
of the Allen–Cahn equation, which can in turn be attained from the
phase field equations.
