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Universal attractor and inertial sets for the phase field model. (English) Zbl 0773.35028
Summary: We consider the phase field equations in dimensions 1, 2 and 3. We show that it is well-posed when assuming that the initial data is square integrable and prove the existence of a universal attractor and of inertial sets.

MSC:
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
35K45 Initial value problems for second-order parabolic systems
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[1] Caginalp, G., Stefan and Hele-Shaw type models as asymptotic limits of the phase field equations, Physical review, A-39, 5887-5896, (1989) · Zbl 1027.80505
[2] D. Brochet, X. Chen and D. Hillhorst, Finite dimensional exponential attractor for the phase field model, (to appear).
[3] Eden, A.; Foias, C.; Nicolaenko, B.; Temam, R., Ensembles inertiels pour des équations d’évolution dissipatives, C.R. acad. sci. Paris, 310, 559-562, (1990) · Zbl 0707.35017
[4] Eden, A.; Milani, A.J.; Nicolaenko, B., Finite dimensional exponential attractors for semilinear wave equations with damping, IMA preprint series, (1990), No. 693 · Zbl 0796.35143
[5] Temam, R., Infinite dimensional dynamical systems in mechanics and physics, () · Zbl 0662.35001
[6] Elliott, C.M.; Zheng, S., Global existence and stability of solutions to the phase field equations in free boundary problems, ()
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