Quarterly of Applied Mathematics

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		Online ISSN 1552-4485; Print ISSN 0033-569X

Solid-liquid phase changes with different densities

Author(s): Michel Frémond; Elisabetta Rocca
Journal: Quart. Appl. Math. 66 (2008), 609-632.
MSC (2000): Primary 80A22, 34A34, 74G25
Posted: September 10, 2008
MathSciNet review: 2465138
Retrieve article in: PDF

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Abstract: In this paper we present a new thermodynamically consistent phase transition model describing the evolution of a liquid substance, e.g., water, in a rigid container $\Omega$ when we freeze the container. Since the density $\varrho_{2}$ of ice with volume fraction $\beta_{2}$ is lower than the density $\varrho_{1}$ of water with volume fraction $\beta_{1}$ , experiments, for instance the freezing of a glass bottle filled with water, show that the water pressure increases up to the rupture of the bottle. When the container is not impermeable, freezing may produce a nonhomogeneous material, for instance water, ice or sorbet. Here we describe a general class of phase transition processes, including this example as a particular case. Moreover, we study the resulting nonlinear and singular PDE system from the analytical viewpoint, recovering existence of a global (in time) weak solution and also uniqueness for some particular choices of the nonlinear functions involved.

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