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

Brochet, D.; Hilhorst, D.; Novick-Cohen, A.

Appl. Math. Lett. 7, No. 3, 83-87 (1994).

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.

MSC:

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

Keywords:

phase separation dynamics; maximal attractor; inertial sets; fractal dimension

References:

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