Publication Date:
2009
Citation:
A bottle in a freezer / P. Krejci, E. Rocca, J. Sprekels. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 41:5(2009), pp. 1851-1873.
abstract:
We propose here a model for solidification of the liquid content of an elastic bottle
in a freezer. The main goal is to explain the occurrence of high stresses inside the bottle. As a byproduct,
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.
in a freezer. The main goal is to explain the occurrence of high stresses inside the bottle. As a byproduct,
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.
IRIS type:
01 - Articolo su periodico
List of contributors:
P. Krejci, E. Rocca, J. Sprekels
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