Long time behaviour of a singular phase transition model

Pavel Krejčí; Jürgen Sprekels

doi:10.3934/dcds.2006.15.1119

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2006, Volume 15, Issue 4: 1119-1135. Doi: 10.3934/dcds.2006.15.1119

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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

Received: April 2005

Revised: October 2005

Published: October 2006

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Abstract

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.

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Mathematics Subject Classification: Primary: 80A22, 35K50; Secondary: 45K05, 35B40, 35B50.

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