|
This article is cited in 7 scientific papers (total in 7 papers)
Research Papers
A variational problem of phase transitions for a two-phase elastic medium with zero coefficient of surface tension
V. G. Osmolovskiĭ
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.
Keywords:
free surfaces, nonconvex variational problems, phase transitions in continuum mechanics.
Received: 30.06.2010
Citation:
V. G. Osmolovskiǐ, “A variational problem of phase transitions for a two-phase elastic medium with zero coefficient of surface tension”, Algebra i Analiz, 22:6 (2010), 214–234; St. Petersburg Math. J., 22:6 (2011), 1007–1022
Linking options:
https://www.mathnet.ru/eng/aa1220 https://www.mathnet.ru/eng/aa/v22/i6/p214
|
Statistics & downloads: |
Abstract page: | 395 | Full-text PDF : | 104 | References: | 43 | First page: | 9 |
|