, Volume 4, Issue 2, pp 375-398

Inertial manifolds and inertial sets for the phase-field equations

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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.

This work was completed while the authors were visiting the Institute for Mathematics and its Applications at the University of Minnesota, Minneapolis, Minnesota 55455.