On the solvability of a variational problem about phase transitions in continuum mechanics

Research output

Abstract

We study a variational problem about phase transitions in continuum mechanics under the condition that the surface tension coefficient vanishes. A homogeneous isotropic two-phase elastic medium occupies a ball-shaped domain, the zero displacement field is fixed on the boundary of this domain, and a spherically symmetric force field acts on the medium. The solvability of this problem is established. As is shown, if a force field is nonzero almost everywhere, then the problem has only spherically symmetric solutions. Bibliography: 9 titles.

Original languageEnglish
Pages (from-to)632-643
Number of pages12
JournalJournal of Mathematical Sciences
Volume156
Issue number4
DOIs
Publication statusPublished - 1 Jan 2009

Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

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