WIAS Preprint No. 1055, (2005)

Pointwise asymptotic convergence of solutions for a phase separation model



Authors

  • Krejčí, Pavel
  • Zheng, Songmu

2010 Mathematics Subject Classification

  • 80A22 35K50 35B40

Keywords

  • Phase-field system, asymptotic phase separation, energy, entropy

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.

Appeared in

  • Discrete Contin. Dyn. Syst., 16 (2006) pp. 1-18.

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