A bottle in a freezer

Details A bottle in a freezer A bottle in a freezer

2009-04-28

arxiv.org/abs/0904.4380v1

SIAM J. Math. Anal., 41 No. 5 (2009), 1851-1873

Mathematics

Analysis of PDEs

Scientific paper

We propose here a model for solidification of a liquid contents of an elastic bottle in a freezer. The main goal is to explain the occurrence of high stresses inside the bottle. As a by-product, we derive a formula for the undercooling coefficient in terms of the elasticity constants, latent heat, and the phase expansion coefficient. We investigate the well-posedness of the three-dimensional model: we prove the existence and uniqueness of a solution for the corresponding initial-boundary value problem which couples a PDE with an integrodifferential equation and an ordinary differential inclusion ruling the evolution of the phase parameter. Finally, we prove some results on the long time behavior of solutions.

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