We consider a variational problem describing two-phase elastic media with nonconstant temperature fields and obtain sufficient conditions for the lower and upper temperatures to be not equal. Bibliography: 5 titles.
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M. A. Grinfel’d, Methods of Continuum Mechanics in the Theory of Phase Transitions [in Russian], Nauka, Moscow (1990).
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, “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).
L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, New York etc. (1992).
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Translated from Problems in Mathematical Analysis 44, January 2010, pp. 93–98.
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Osmolovskii, V.G. On the nonexistence zone of one-phase equilibrium states of a phase transition problem of continuum mechanics in the case of nonconstant temperature fields. J Math Sci 165, 105–109 (2010). https://doi.org/10.1007/s10958-010-9783-6
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DOI: https://doi.org/10.1007/s10958-010-9783-6