A variational problem of phase transitions for a two-phase elastic medium with zero coefficient of surface tension
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V. G. Osmolovskiĭ
Translated by: N. B. Lebedinskaya - St. Petersburg Math. J. 22 (2011), 1007-1022
- DOI: https://doi.org/10.1090/S1061-0022-2011-01181-1
- Published electronically: August 22, 2011
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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.References
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Bibliographic Information
- V. G. Osmolovskiĭ
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskaya Ul. 28, Stary Petergof, St. Petersburg 198504, Russia
- Email: vicos@VO8167.spb.edu
- Received by editor(s): June 30, 2010
- Published electronically: August 22, 2011
- Additional Notes: Supported by RFBR (grant no. 08-01-00748)
- © Copyright 2011 American Mathematical Society
- Journal: St. Petersburg Math. J. 22 (2011), 1007-1022
- MSC (2010): Primary 74B05
- DOI: https://doi.org/10.1090/S1061-0022-2011-01181-1
- MathSciNet review: 2760092
Dedicated: Dedicated to Vasiliĭ Mikhaĭlovich Babich