Phase Transitions with Semi-Diffuse Interfaces





James M. Greenberg
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
greenber@andrew.cmu.edu








In this paper we examine new ``phase-field" models with semi-diffuse interfaces. These models have the property that the $ -1/+1$ planar phase transitions take place over a finite interval. The models also support multiple interface solutions with interfaces centered at arbitrary points $ L_1 < L_2 < \ldots < L_N$. The classical models have no such exact solutions. These stationary solutions are minima of the entropy functional which characterizes the system and are dynamically stable.


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