Well-posedness of an extended model for water-ice phase transitions

0383891 - MÚ 2013 RIV US eng J - Článek v odborném periodiku
Krejčí, Pavel - Rocca, E.
Well-posedness of an extended model for water-ice phase transitions.
Discrete and Continuous Dynamical systems - Series S. Roč. 6, č. 2 (2013), s. 439-460. ISSN 1937-1632. E-ISSN 1937-1179
Grant CEP: GA ČR GAP201/10/2315
Institucionální podpora: RVO:67985840
Klíčová slova: phase transitions * nonlocal problems * uniqueness
Kód oboru RIV: BA - Obecná matematika
http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=7900

We propose an improved model explaining the occurrence of high stresses due to the diff erence in speci fic volumes during phase transitions between water and ice. The unknowns of the resulting evolution problem are the absolute temperature, the volume increment, and the liquid fraction. The main novelty here consists in including the dependence of the speci fic heat and of the speed of sound upon the phase. These additional nonlinearities bring new mathematical difficulties which require new estimation techniques based on Moser iteration. We establish the existence of a global solution to the corresponding initial-boundary value problem, as well as lower and upper bounds for the absolute temperature. Assuming constant heat conductivity, we also prove uniqueness and continuous data dependence of the solution.
Trvalý link: http://hdl.handle.net/11104/0213688