{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:51:58Z","timestamp":1777449118429,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2014,5,1]],"date-time":"2014-05-01T00:00:00Z","timestamp":1398902400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2014,5]]},"abstract":"<jats:p>We build a predictive theory for the evolution of mixture of helium and supercooled helium at low temperature. The absolute temperature \u03b8 and the volume fraction \u03b2 of helium, which is dominant at temperature larger than the phase change temperature, are the state quantities. The predictive theory accounts for local interactions at the microscopic level, involving the gradient of \u03b2. The nonlinear heat flux in the supercooled phase results from a Norton\u2013Hoff potential. We prove that the resulting set of partial differential equations has solutions within a convenient analytical frame.<\/jats:p>","DOI":"10.3233\/asy-131195","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:32:04Z","timestamp":1575055924000},"page":"29-42","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["A phase transition model for the helium supercooling"],"prefix":"10.1177","volume":"87","author":[{"given":"Elena","family":"Bonetti","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Pavia, via Ferrata 1, 27100 Pavia, Italy. E-mail: elena.bonetti@unipv.it"}]},{"given":"Michel","family":"Fr\u00e9mond","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria Civile, Universit\u00e0 di Roma \u201cTor Vergata\u201d, via del Politecnico 1, 00133 Roma, Italy. E-mail: michel.fremond@uniroma2.it"}]}],"member":"179","published-online":{"date-parts":[[2014,5,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-131195","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-131195","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:05Z","timestamp":1777380005000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-131195"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2014,5]]}},"alternative-id":["10.3233\/ASY-131195"],"URL":"https:\/\/doi.org\/10.3233\/asy-131195","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5]]}}}