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Inertial manifolds and inertial sets for the phasefield equations
 Peter W. Bates,
 Songmu Zheng
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The phasefield 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 lowdimensional space, the flow is essentially finite dimensional in the sense that a strongly attracting finitedimensional 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.
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 Title
 Inertial manifolds and inertial sets for the phasefield equations
 Journal

Journal of Dynamics and Differential Equations
Volume 4, Issue 2 , pp 375398
 Cover Date
 19920401
 DOI
 10.1007/BF01049391
 Print ISSN
 10407294
 Online ISSN
 15729222
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 Parabolic
 attractor
 infinitedimensional dynamical system
 global existence and regularity
 Authors

 Peter W. Bates ^{(1)} ^{(2)}
 Songmu Zheng ^{(3)}
 Author Affiliations

 1. Department of Mathematics, Brigham Young University, 84602, Provo, Utah
 2. Currently visiting the Department of Mathematics, University of Utah, 84112, Salt Lake City, Utah
 3. Institute of Mathematics, Fudan University, Shanghai, PRC