Research output: Contribution to journal › Article › peer-review
A variational problem of phase transitions for a two-phase elastic medium with zero coefficient of surface tension. / Osmolovskiǐ, V. G.
In: St. Petersburg Mathematical Journal, Vol. 22, No. 6, 01.12.2011, p. 1007-1022.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 42741333