Elastoplastic reaction of a container to water freezing

Pavel Krejčí

Mathematica Bohemica (2010)

  • Volume: 135, Issue: 4, page 423-441
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Krejčí, Pavel. "Elastoplastic reaction of a container to water freezing." Mathematica Bohemica 135.4 (2010): 423-441. <http://eudml.org/doc/196947>.

@article{Krejčí2010,
abstract = {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.},
author = {Krejčí, Pavel},
journal = {Mathematica Bohemica},
keywords = {phase transition; water; ice; energy; entropy; elastoplastic boundary; phase transition; water; ice; energy; entropy; elastoplastic boundary},
language = {eng},
number = {4},
pages = {423-441},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Elastoplastic reaction of a container to water freezing},
url = {http://eudml.org/doc/196947},
volume = {135},
year = {2010},
}

TY - JOUR
AU - Krejčí, Pavel
TI - Elastoplastic reaction of a container to water freezing
JO - Mathematica Bohemica
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 135
IS - 4
SP - 423
EP - 441
AB - 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.
LA - eng
KW - phase transition; water; ice; energy; entropy; elastoplastic boundary; phase transition; water; ice; energy; entropy; elastoplastic boundary
UR - http://eudml.org/doc/196947
ER -

References

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  1. Brokate, M., Sprekels, J., 10.1007/978-1-4612-4048-8_5, Appl. Math. Sci. 121, Springer, New York (1996). (1996) Zbl0951.74002MR1411908DOI10.1007/978-1-4612-4048-8_5
  2. Frémond, M., Non-Smooth Thermo-Mechanics, Springer, Berlin (2002). (2002) MR1885252
  3. Frémond, M., Rocca, E., 10.1142/S0218202506001261, Math. Models Methods Appl. Sci. 16 (2006), 559-586. (2006) Zbl1105.80007MR2218214DOI10.1142/S0218202506001261
  4. Frémond, M., Rocca, E., 10.1090/S0033-569X-08-01100-0, Q. Appl. Math. 66 (2008), 609-632. (2008) Zbl1157.80385MR2465138DOI10.1090/S0033-569X-08-01100-0
  5. Krasnosel'skii, M. A., Pokrovskii, A. V., Systems with Hysteresis, Springer, Berlin (1989). (1989) Zbl0665.47038MR0987431
  6. Krejčí, P., Hysteresis operators---a new approach to evolution differential inequalities, Comment. Math. Univ. Carolinae 33 (1989), 525-536. (1989) MR1031870
  7. Krejčí, P., Hysteresis, Convexity and Dissipation in Hyperbolic Equations, Gakuto Int. Series. Math. Sci. Appl., Vol. 8, Gakkotosho, Tokyo (1996). (1996) MR2466538
  8. Krejčí, P., Rocca, E., Sprekels, J., 10.1137/09075086X, SIAM J. Math. Anal. 41 (2009), 1851-1873. (2009) Zbl1202.80014MR2564197DOI10.1137/09075086X
  9. Krejčí, P., Rocca, E., Sprekels, J., Phase separation in a gravity field, (to appear) in DCDS-S. MR2746380
  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. (2010) 
  11. Visintin, A., Models of Phase Transitions, Progress in Nonlinear Differential Equations and their Applications 28, Birkhäuser, Boston (1996). (1996) Zbl0882.35004MR1423808

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