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Journal of the London Mathematical Society Advance Access originally published online on August 31, 2007
Journal of the London Mathematical Society 2007 76(1):197-210; doi:10.1112/jlms/jdm032
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© 2007 London Mathematical Society

Non-local temperature-dependent phase-field models for non-isothermal phase transitions

Pavel Krejcí

Weierstrass Institute for Applied Analysis and Stochastics
Mohrenstr. 39
D-10117 Berlin
Germany
krejci{at}wias-berlin.de
and
Mathematical Institute
Czech Academy of Sciences
Zitná 25
CZ-11567 Praha 1
Czech Republic
krejci{at}math.cas.cz

Elisabetta Rocca

Dipartimento di Matematica
Università di Milano
Via Saldini 50
20133 Milano
Italy
rocca{at}mat.unimi.it

Jürgen Sprekels

Weierstrass Institute for Applied Analysis and Stochastics
Mohrenstr. 39
D-10117 Berlin
Germany

We propose a model for non-isothermal phase transitions with non-con-served order parameter driven by a spatially non-local 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.

sprekels{at}wias-berlin.de

2000 Mathematics Subject Classification 80A22 (primary), 45K05, 35B50 (secondary).

The work was done during the second author's stay at WIAAS Berlin in November 2004.

Received September 5, 2006; published online August 31, 2007.


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