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November  2006, 15(4): 1119-1135. doi: 10.3934/dcds.2006.15.1119

Long time behaviour of a singular phase transition model

Pavel Krejčí 1, and  Jürgen Sprekels 1,

1. 

Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D–10117 Berlin, Germany

Received  April 2005 Revised  October 2005 Published  May 2006

A phase-field system, non-local in space and non-smooth in time, with heat flux proportional to the gradient of the inverse temperature, is shown to admit a unique strong thermodynamically consistent solution on the whole time axis. The temperature remains globally bounded both from above and from below, and its space gradient as well as the time derivative of the order parameter asymptotically vanish in $L^2$-norm as time tends to infinity.
Keywords: long-time behaviour., Phase transition, nonlocal model, integrodifferential heat equation.
Mathematics Subject Classification: Primary: 80A22, 35K50; Secondary: 45K05, 35B40, 35B5.
Citation: Pavel Krejčí, Jürgen Sprekels. Long time behaviour of a singular phase transition model. Discrete and Continuous Dynamical Systems, 2006, 15 (4) : 1119-1135. doi: 10.3934/dcds.2006.15.1119
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