Finite dimensional exponential attractor for the phase field model. (English) Zbl 0790.35052

We consider the phase field equations in arbitrary space dimension. We show that the corresponding boundary value problems are well-posed when assuming that the initial data is square integrable and prove the existence of a maximal attractor and of an inertial set.


35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B40 Asymptotic behavior of solutions to PDEs
Full Text: DOI Link


[1] Bates P., IMA preprint (1991)
[2] DOI: 10.1016/0893-9659(91)90076-8 · Zbl 0773.35028
[3] DOI: 10.1007/BF00254827 · Zbl 0608.35080
[4] Eden A., C.R. Acad. Sci. Paris 310 pp 559– (1990)
[5] Eden A., Finite dimensional exponential attractors for semi-linear wave equations with damping IMA Preprint 693 (1990)
[6] Elliott C.M., Global existence and stability of solutions to the phase field equations, in Free Boundary Problems 95 (1990) · Zbl 0733.35062
[7] Ladyzenskaja O.A., Translations of Mathematical Monographs 23 (1968)
[8] Lions J.L., Nonhomogeneous Boundary Value Problems and Applications (1972)
[9] DOI: 10.1080/00036818708839678 · Zbl 0609.35009
[10] Temam R., Infinite Dimensional Dynamical Systems in Mechanics and Physics 68 (1988) · Zbl 0662.35001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.