Finite-dimensional exponential attractor for a model for order-disorder and phase separation. (English) Zbl 0803.35076

Summary: We consider a system of equations for simultaneous order-disorder and phase separation dynamics in space dimensions \(N = 1\), 2 and 3 and show that the correct corresponding boundary value problem with homogeneous Neumann boundary conditions is well-posed. We then prove the existnce of maximal attractor and of inertial sets so that we also obtain an upper bound for the fractal dimension of the attractor.


35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
35K35 Initial-boundary value problems for higher-order parabolic equations
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
76T99 Multiphase and multicomponent flows
Full Text: DOI


[2] Eden, A.; Foias, C.; Nicolaenko, B.; Temam, R., Ensembels inertiels pour des équations d’évolution dissipatives sets, C.R. Acad. Sci. Paris, 310, 559-562 (1990) · Zbl 0707.35017
[3] Eden, A.; Foias, C.; Nicolaenko, B.; Temam, R., Inertial sets for dissipative evolution equations Part I: Construction and applications, IMA Preprint Series, No. 812 (May 1991)
[4] Eden, A.; Milani, A. J.; Nicolaenko, B., Finite dimensional exponential attractors for semilinear wave equations with damping, IMA Preprint Series, No. 693 (1990) · Zbl 0796.35143
[6] Brochet, D.; Hilhorst, D., Universal attractor and inertial sets for the phase field model, Appl. Math. Lett., 4, 6, 59-62 (1991) · Zbl 0773.35028
[8] Temam, R., Infinite Dimensional Dynamical System in Mechanics and Physics, (Applied Mathematical Sciences, 68 (1988), Springer: Springer New York) · Zbl 0523.49030
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.