35B50 Maximum principles
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Year of publication
- 2006 (2)
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- English (2)
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- C17 (2)
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- C (2)
We propose a model for non-isothermal phase
transitions with non-conserved order parameter driven by
a spatially nonlocal free energy with respect to both the
temperature and the order parameter. The resulting system of equations
is shown to be thermodynamically consistent and to admit a strong
solution.
We prove the existence, uniqueness, thermodynamic consistency,
global boundedness from both above and below, and continuous data
dependence for a strong solution to an
integrodifferential model for nonisothermal phase transitions
under nonhomogeneous mixed boundary conditions.
The specific heat is allowed to depend on the order parameter,
and the convex component of the free energy may or may not
be singular.