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• W2964133785 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 <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Omega> <mml:semantics> <mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi> <mml:annotation encoding=application/x-tex>Omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula> when we freeze the container. Since the density <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=rho 2> <mml:semantics> <mml:msub> <mml:mi>ϱ<!-- ϱ --></mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:annotation encoding=application/x-tex>varrho _{2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of ice with volume fraction <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=beta 2> <mml:semantics> <mml:msub> <mml:mi>β<!-- β --></mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:annotation encoding=application/x-tex>beta _{2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is lower than the density <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=rho 1> <mml:semantics> <mml:msub> <mml:mi>ϱ<!-- ϱ --></mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:annotation encoding=application/x-tex>varrho _{1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of water with volume fraction <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=beta 1> <mml:semantics> <mml:msub> <mml:mi>β<!-- β --></mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:annotation encoding=application/x-tex>beta _{1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, 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." @default.
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• W2964133785 date "2008-09-10" @default.
• W2964133785 modified "2023-09-26" @default.
• W2964133785 title "Solid-liquid phase changes with different densities" @default.
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• W2964133785 doi "https://doi.org/10.1090/s0033-569x-08-01100-0" @default.
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