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

Pavel Krejčí; Elisabetta Rocca

doi:10.3934/dcdss.2013.6.439

Article Contents

2013, Volume 6, Issue 2: 439-460. Doi: 10.3934/dcdss.2013.6.439

This issue Previous Article Parabolic quasi-variational diffusion problems with gradient constraints Next Article Equilibrium and stability of tensegrity structures: A convex analysis approach

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

Pavel Krejčí^1, and
Elisabetta Rocca^2,

1.
Institute of Mathematics, Czech Academy of Sciences, Žitná 25, CZ-11567 Praha 1
2.
WIAS Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, Germany, Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano

Received: June 30, 2011

Revised: November 30, 2011

Published: March 2013

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Abstract

We propose an improved model explaining the occurrence of high stresses due to the difference in specific 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 specific 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.

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Mathematics Subject Classification: 82B26, 34B10, 74G25, 74G30, 74G45.

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