Pointwise asymptotic convergence of solutions for a phase separation model
Pavel Krejčí - Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D–10117 Berlin, Germany (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.
Received: September 2005; Revised: February 2006; Available Online: June 2006.
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