Previous |  Up |  Next


phase transition; water; ice; energy; entropy; elastoplastic boundary
The paper deals with a model for water freezing in a deformable elastoplastic container. The mathematical problem consists of a system of one parabolic equation for temperature, one integrodifferential equation with a hysteresis operator for local volume increment, and one differential inclusion for the water content. The problem is shown to admit a unique global uniformly bounded weak solution.
[1] Brokate, M., Sprekels, J.: Hysteresis and Phase Transitions. Appl. Math. Sci. 121, Springer, New York (1996). DOI 10.1007/978-1-4612-4048-8_5 | MR 1411908 | Zbl 0951.74002
[2] Frémond, M.: Non-Smooth Thermo-Mechanics. Springer, Berlin (2002). MR 1885252
[3] Frémond, M., Rocca, E.: Well-posedness of a phase transition model with the possibility of voids. Math. Models Methods Appl. Sci. 16 (2006), 559-586. DOI 10.1142/S0218202506001261 | MR 2218214 | Zbl 1105.80007
[4] Frémond, M., Rocca, E.: Solid-liquid phase changes with different densities. Q. Appl. Math. 66 (2008), 609-632. DOI 10.1090/S0033-569X-08-01100-0 | MR 2465138 | Zbl 1157.80385
[5] Krasnosel'skii, M. A., Pokrovskii, A. V.: Systems with Hysteresis. Springer, Berlin (1989). MR 0987431 | Zbl 0665.47038
[6] Krejčí, P.: Hysteresis operators---a new approach to evolution differential inequalities. Comment. Math. Univ. Carolinae 33 (1989), 525-536. MR 1031870
[7] Krejčí, P.: Hysteresis, Convexity and Dissipation in Hyperbolic Equations. Gakuto Int. Series. Math. Sci. Appl., Vol. 8, Gakkotosho, Tokyo (1996). MR 2466538
[8] Krejčí, P., Rocca, E., Sprekels, J.: A bottle in a freezer. SIAM J. Math. Anal. 41 (2009), 1851-1873. DOI 10.1137/09075086X | MR 2564197 | Zbl 1202.80014
[9] Krejčí, P., Rocca, E., Sprekels, J.: Phase separation in a gravity field. (to appear) in DCDS-S. MR 2746380
[10] Krejčí, P., Rocca, E., Sprekels, J.: Liquid-solid phase transitions in a deformable container. Continuous Media with Microstructure (B. Albers, ed.). Springer, Berlin (2010), 281-296.
[11] Visintin, A.: Models of Phase Transitions. Progress in Nonlinear Differential Equations and their Applications 28, Birkhäuser, Boston (1996). MR 1423808 | Zbl 0882.35004
Partner of
EuDML logo