# American Institute of Mathematical Sciences

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

## Pointwise asymptotic convergence of solutions for a phase separation model

 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.
Citation: Pavel Krejčí, Songmu Zheng. Pointwise asymptotic convergence of solutions for a phase separation model. Discrete & Continuous Dynamical Systems - A, 2006, 16 (1) : 1-18. doi: 10.3934/dcds.2006.16.1
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