### Abstract

We prove that any global bounded solution of a phase field model tends to a single equilibrium state for large times though the set of equilibria may contain a nontrivial continuum of stationary states. The problem has a partial variational structure, specifically, only the elliptic part of the first equation represents an Euler-Lagrange equation while the second does not. This requires some modifications in comparison with standard methods used to attack this kind of problems.

Original language | English |
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Pages (from-to) | 277-287 |

Number of pages | 11 |

Journal | Mathematical Methods in the Applied Sciences |

Volume | 24 |

Issue number | 5 |

DOIs | |

Publication status | Published - Mar 25 2001 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Engineering(all)

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## Cite this

Milani, A., & Han, Y. (2001). Long-time convergence of solutions to a phase-field system.

*Mathematical Methods in the Applied Sciences*,*24*(5), 277-287. https://doi.org/10.1002/mma.215