# Inertial manifolds and inertial sets for the phase-field equations

Article

DOI: 10.1007/BF01049391

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

- 32 Citations
- 62 Downloads

## Abstract

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 H^{1}×L^{2} 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