Journal of Dynamics and Differential Equations

, Volume 4, Issue 2, pp 375–398

Inertial manifolds and inertial sets for the phase-field equations

  • Peter W. Bates
  • Songmu Zheng

DOI: 10.1007/BF01049391

Cite this article as:
Bates, P.W. & Zheng, S. J Dyn Diff Equat (1992) 4: 375. doi:10.1007/BF01049391


The phase-field system is a mathematical model of phase transition, coupling temperature with a continuous order parameter which describes degree of solidification. The flow induced by this system is shown to be smoothing in H1×L2 and a global attractor is shown to exist. Furthermore, in low-dimensional space, the flow is essentially finite dimensional in the sense that a strongly attracting finite-dimensional manifold (or set) exists.

Key words

Parabolicattractorinfinite-dimensional dynamical systemglobal existence and regularity

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • Peter W. Bates
    • 1
    • 2
  • Songmu Zheng
    • 3
  1. 1.Department of MathematicsBrigham Young UniversityProvo
  2. 2.Currently visiting the Department of MathematicsUniversity of UtahSalt Lake City
  3. 3.Institute of MathematicsFudan UniversityShanghaiPRC