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Long-time behaviour for a model of phase-field type

  • Ph. Laurençot (a1)
Abstract

In this paper, we study a model of phase-field type for the kinetics of phase transitions which was considered by Halperin, Hohenberg and Ma and which includes the phase-field equations. We study the well-posedness of the corresponding initial boundary value problem in an open bounded subset in space dimension lower than or equal to 3 and prove that, under suitable conditions, the long-time behaviour of the solutions to this problem is described by a maximal attractor.

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3 H. Amann . Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems. In Function Spaces, Differential Operators and Nonlinear Analysis, eds H. Triebel and H. J. Schmeisser Teubner-Texte Math. 133, 9126 (Stuttgart: Teubner, 1993).

14 R. Temam . Infinite-dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Sciences 68 (New York: Springer, 1988).

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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