{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:36:40Z","timestamp":1787323000045,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>We propose here a model for solidification of the liquid content of an elastic bottle in a freezer. The main goal is to explain the occurrence of high stresses inside the bottle. As a by-product, we derive a formula for the undercooling coefficient in terms of the elasticity constants, latent heat, and the phase expansion coefficient. We investigate the well-posedness of the three-dimensional model: we prove the existence and uniqueness of a solution for the corresponding initial-boundary value problem which couples a PDE with an integrodifferential equation and an ordinary differential inclusion ruling the evolution of the phase parameter. Finally, we prove some results on the long time behavior of solutions.<\/jats:p>","DOI":"10.1137\/09075086x","type":"journal-article","created":{"date-parts":[[2009,11,11]],"date-time":"2009-11-11T18:31:07Z","timestamp":1257964267000},"page":"1851-1873","source":"Crossref","is-referenced-by-count":5,"title":["A Bottle in a Freezer"],"prefix":"10.1137","volume":"41","author":[{"given":"Pavel","family":"Krej\u010d\u00ed","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elisabetta","family":"Rocca","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00fcrgen","family":"Sprekels","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,11,11]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.21136\/CMJ.1994.128452"},{"key":"R2","unstructured":"H. Brezis,\n                      Op\u00e9rateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert\n                      , North\u2013Holland Math. Stud. 5, North\u2013Holland, Amsterdam, 1973."},{"key":"R3","doi-asserted-by":"crossref","unstructured":"M. Brokate and J. Sprekels,\n                      Hysteresis and Phase Transitions\n                      , Appl. Math. Sci. 121, Springer, New York, 1996.","DOI":"10.1007\/978-1-4612-4048-8"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/1040232"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"M. Fr\u00e9mond,\n                      Nonsmooth Thermomechanics\n                      , Springer-Verlag, Berlin, 2002.","DOI":"10.1007\/978-3-662-04800-9"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202506001261"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1090\/S0033-569X-08-01100-0"},{"key":"R8","unstructured":"C. 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Visintin,\n                      Models of Phase Transitions\n                      , Progr. Nonlinear Differential Equations Appl. 28, Birkh\u00e4user Boston, Inc., Boston, MA, 1996."},{"key":"R22","unstructured":"H. Yildirim Erbil,\n                      Surface Chemistry of Solid and Liquid Interfaces\n                      , Blackwell Publishing, Oxford, UK, 2006."}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/09075086X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:36:34Z","timestamp":1787319394000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/09075086X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":22,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/09075086X"],"URL":"https:\/\/doi.org\/10.1137\/09075086x","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}