Well-posedness of an extended model for water-ice phase transitions
Pavel Krejčı́, Elisabetta Rocca · Discrete and Continuous Dynamical Systems - S · 2012
We propose an improvedmodel explaining the occurrence of high stresses due to thedifference in specific volumes during phase transitions betweenwater and ice. The unknowns of the resulting evolution problem are the absolute temperature,the volume increment, and the liquid fraction. The main novelty here consistsin including the dependence of the specific heat and of the speed of soundupon the phase. These additional nonlinearities bringnew mathematical difficulties which require new estimation techniques based onMoser iteration. We establish the existence of a global solution tothe corresponding initial-boundary value problem, as well as lower andupper bounds for the absolute temperature. Assuming constant heat conductivity,we also prove uniqueness and continuous data dependence of the solution.