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March  2006, 16(1): 1-18. doi: 10.3934/dcds.2006.16.1

Pointwise asymptotic convergence of solutions for a phase separation model

Pavel Krejčí 1, and  Songmu Zheng 2,

1. 

Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D–10117 Berlin
2. 

Institute of Mathematics, Fudan University, Shanghai 200433, China

Received  September 2005 Revised  February 2006 Published  June 2006

A new technique, combining the global energy and entropy balance equations with the local stability theory for dynamical systems, is used for proving that every solution to a non-smooth temperature-driven phase separation model with conserved energy converges pointwise in space to an equilibrium as time tends to infinity. Three main features are observed: the limit temperature is uniform in space, there exists a partition of the physical body into at most three constant limit phases, and the phase separation process has a hysteresis-like character.
Keywords: Phase-field system, asymptotic phase separation, entropy., energy.
Mathematics Subject Classification: Primary: 80A22, 35K50; Secondary: 35B4.
Citation: Pavel Krejčí, Songmu Zheng. Pointwise asymptotic convergence of solutions for a phase separation model. Discrete & Continuous Dynamical Systems, 2006, 16 (1) : 1-18. doi: 10.3934/dcds.2006.16.1
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