On the singular limit in a phase field model of phase transitions

  • Nicholas D. Alikakos

    Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
  • Peter W. Bates

    Department of Mathematics, Brigham Young University, Provo, Utah 84602


The limits of families of stable solutions for the equation over radially symmetric domains with no-flux boundary conditions are discribed. Particular emphasis is placed on the characterization of points of discontinuity of these limits (interfaces) and on the description of the graph of for small . Sufficient conditions for existence of interfaces in terms of the temperature function, , are given. The analysis is more complete for families of global minimizers of the associated energy functional.


On étudie les limites de familles de solutions stables de l’équation sur des domaines à symétrie radiale sans flux au bord. On s’attache particulièrement à caractériser les points de discontinuité de ces limites (interfaces) et à décrire le graphe de pour petit . On donne des conditions suffisantes sur la température T pour qu’il existe des interfaces. On analyse de manière plus approfondie les familles minimisant l’énergie totale.

Cite this article

Nicholas D. Alikakos, Peter W. Bates, On the singular limit in a phase field model of phase transitions. Ann. Inst. H. Poincaré Anal. Non Linéaire 5 (1988), no. 2, pp. 141–178

DOI 10.1016/S0294-1449(16)30349-3