A variational problem of phase transitions for a two-phase elastic medium with zero coefficient of surface tension

Research output

4 Citations (Scopus)

Abstract

The variational problem on the equilibrium of a two-phase elastic medium is given in an extended form and is compared with the standard setting. The lower semicontinuity of the energy functional in the extended formulation is studied, and an example is constructed where no equilibrium states exist for a special class of residual strain tensors. In the case of isotropic media, a method is described for finding equilibrium states in explicit form. The notion of temperatures of phase transitions is introduced, their existence is proved, and their properties are studied.

Original languageEnglish
Pages (from-to)1007-1022
Number of pages16
JournalSt. Petersburg Mathematical Journal
Volume22
Issue number6
DOIs
Publication statusPublished - 1 Dec 2011

Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Applied Mathematics

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