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 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.
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This work was completed while the authors were visiting the Institute for Mathematics and its Applications at the University of Minnesota, Minneapolis, Minnesota 55455.
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Bates, P.W., Zheng, S. Inertial manifolds and inertial sets for the phase-field equations. J Dyn Diff Equat 4, 375–398 (1992). https://doi.org/10.1007/BF01049391
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DOI: https://doi.org/10.1007/BF01049391