A general class of phase transition models with weighted interface energy

  • E. Acerbi

    Dipartimento di Matematica, Università di Parma, Viale G.P. Usberti 53a, 43100 Parma, Italy
  • G. Bouchitté

    UFR Sciences, Université du Sud-Toulon-Var, BP 20132, 83957 La Garde Cedex, France

Abstract

We study a family of singular perturbation problems of the kind

where represents a fluid density and the non-negative energy density vanishes only for or . The novelty of the model is the additional variable which is also unknown and interplays with the gradient of in the formation of interfaces. Under mild assumptions on , we characterize the limit energy as and find for each a transition energy (well defined when and is a measure) which depends on the dimensional density of the measure on the jump set of . An explicit formula is also given.

Cite this article

E. Acerbi, G. Bouchitté, A general class of phase transition models with weighted interface energy. Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008), no. 6, pp. 1111–1143

DOI 10.1016/J.ANIHPC.2007.09.004