TY - JOUR

T1 - A variational problem of phase transitions for a two-phase elastic medium with zero coefficient of surface tension

AU - Osmolovskiǐ, V. G.

PY - 2011/12/1

Y1 - 2011/12/1

N2 - 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.

AB - 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.

KW - Free surfaces

KW - Nonconvex variational problems

KW - Phase transitions in continuum mechanics

UR - http://www.scopus.com/inward/record.url?scp=84871403790&partnerID=8YFLogxK

U2 - 10.1090/S1061-0022-2011-01181-1

DO - 10.1090/S1061-0022-2011-01181-1

M3 - Article

AN - SCOPUS:84871403790

VL - 22

SP - 1007

EP - 1022

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 6

ER -