We consider a two-phase elastic medium with zero boundary condition on the displacement field and zero force. We show that the temperatures of phase transitions are independent of the domain occupied by the medium. Bibliography: 6 titles.
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G. Ficera, Existence Theorems in the Theory of Elasticity [in Russian], Mir, Moscow (1974).
V. G. Osmolovskii, “Existence of phase transition temperatures of a nonhomogeneous anisotropic two-phase elastic medium” [in Russian], Probl. Mat. Anal. 31 59-66 (2005); English transl.: J. Math. Sci., New York 132, No. 4, 441–450 (2006).
V. G. Osmolovskii, “On the phase transition temperature in a variational problem of elasticity theory for two-phase media” [in Russian], Probl. Mat. Anal. 41, 37–47 (2009); English transl.: J. Math. Sci., New York 159, No. 2, 168–179 (2009).
V. G. Osmolovskii, “Dependence of the temperature of phase transitions on the size of the domain” [in Russian], Zap. Nauchn. Semin. POMI 310, 98–114 (2004); English transl.: J. Math. Sci., New York 132, No. 3, 304–312 (2006).
V. G. Osmolovskii, “Exact solutions to the variational problem of the phase transition theory in continuum mechanics” [in Russian], Probl. Mat. Anal. 27, 171–206 (2004); English transl.: J. Math. Sci., New York 120, No. 2, 1167–1190 (2004).
V. G. Osmolovskii, “Temperature-dependence of equilibrium states of a two-phase elastic medium with the zero surface tension coefficient” [in Russian], Probl. Mat. Anal. 28, 95–104 (2004); English transl.: J. Math. Sci., New York 122, No. 3, 3278–3289 (2004).
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Translated from Problems in Mathematical Analysis 66, August 2012, pp. 147–151.
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Osmolovskii, V.G. Independence of temperatures of phase transitions of the domain occupied by a two-phase elastic medium. J Math Sci 186, 302–306 (2012). https://doi.org/10.1007/s10958-012-0986-x
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DOI: https://doi.org/10.1007/s10958-012-0986-x