Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Pointwise asymptotic convergence of solutions for a phase separation model

Pages: 1 - 18, Volume 16, Issue 1, September 2006      doi:10.3934/dcds.2006.16.1

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Pavel Krejčí - Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D–10117 Berlin, Germany (email)
Songmu Zheng - Institute of Mathematics, Fudan University, Shanghai 200433, China (email)

Abstract: 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, energy, entropy.
Mathematics Subject Classification:  Primary: 80A22, 35K50; Secondary: 35B40.

Received: September 2005;      Revised: February 2006;      Available Online: June 2006.