| Title:
|
Elastoplastic reaction of a container to water freezing (English) |
| Author:
|
Krejčí, Pavel |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
135 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
423-441 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
phase transition |
| Keyword:
|
water |
| Keyword:
|
ice |
| Keyword:
|
energy |
| Keyword:
|
entropy |
| Keyword:
|
elastoplastic boundary |
| MSC:
|
35K85 |
| MSC:
|
47J40 |
| MSC:
|
80A22 |
| idZBL:
|
Zbl 1224.80019 |
| idMR:
|
MR2681016 |
| DOI:
|
10.21136/MB.2010.140833 |
| . |
| Date available:
|
2010-11-24T08:29:18Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140833 |
| . |
| Reference:
|
[1] Brokate, M., Sprekels, J.: Hysteresis and Phase Transitions.Appl. Math. Sci. 121, Springer, New York (1996). Zbl 0951.74002, MR 1411908, 10.1007/978-1-4612-4048-8_5 |
| Reference:
|
[2] Frémond, M.: Non-Smooth Thermo-Mechanics.Springer, Berlin (2002). MR 1885252 |
| Reference:
|
[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. Zbl 1105.80007, MR 2218214, 10.1142/S0218202506001261 |
| Reference:
|
[4] Frémond, M., Rocca, E.: Solid-liquid phase changes with different densities.Q. Appl. Math. 66 (2008), 609-632. Zbl 1157.80385, MR 2465138, 10.1090/S0033-569X-08-01100-0 |
| Reference:
|
[5] Krasnosel'skii, M. A., Pokrovskii, A. V.: Systems with Hysteresis.Springer, Berlin (1989). Zbl 0665.47038, MR 0987431 |
| Reference:
|
[6] Krejčí, P.: Hysteresis operators---a new approach to evolution differential inequalities.Comment. Math. Univ. Carolinae 33 (1989), 525-536. MR 1031870 |
| Reference:
|
[7] Krejčí, P.: Hysteresis, Convexity and Dissipation in Hyperbolic Equations.Gakuto Int. Series. Math. Sci. Appl., Vol. 8, Gakkotosho, Tokyo (1996). MR 2466538 |
| Reference:
|
[8] Krejčí, P., Rocca, E., Sprekels, J.: A bottle in a freezer.SIAM J. Math. Anal. 41 (2009), 1851-1873. Zbl 1202.80014, MR 2564197, 10.1137/09075086X |
| Reference:
|
[9] Krejčí, P., Rocca, E., Sprekels, J.: Phase separation in a gravity field.(to appear) in DCDS-S. MR 2746380 |
| Reference:
|
[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. |
| Reference:
|
[11] Visintin, A.: Models of Phase Transitions.Progress in Nonlinear Differential Equations and their Applications 28, Birkhäuser, Boston (1996). Zbl 0882.35004, MR 1423808 |
| . |
