Pointwise asymptotic convergence of solutions for a phase separation model

Pavel Krejčí; Songmu Zheng

doi:10.3934/dcds.2006.16.1

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2006, Volume 16, Issue 1: 1-18. Doi: 10.3934/dcds.2006.16.1 open access

This issue Previous Article Next Article Decay of correlations for non-Hölder observables

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

Received: August 31, 2005

Revised: January 31, 2006

Published: February 2006

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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.

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

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