### 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 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Engineering(all)

### Cite this

*Mathematical Methods in the Applied Sciences*,

*24*(5), 277-287. https://doi.org/10.1002/mma.215

}

*Mathematical Methods in the Applied Sciences*, vol. 24, no. 5, pp. 277-287. https://doi.org/10.1002/mma.215

**Long-time convergence of solutions to a phase-field system.** / Milani, Albert; Han, Yang.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Long-time convergence of solutions to a phase-field system

AU - Milani, Albert

AU - Han, Yang

PY - 2001/3/25

Y1 - 2001/3/25

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035946157&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035946157&partnerID=8YFLogxK

U2 - 10.1002/mma.215

DO - 10.1002/mma.215

M3 - Article

VL - 24

SP - 277

EP - 287

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 5

ER -