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The finite dimensional attractor for a 4th order system of cahn-hilliard type with a supercritical nonlinearity

Efendiev, MA, Gajewski, H and Zelik, S (2002) The finite dimensional attractor for a 4th order system of cahn-hilliard type with a supercritical nonlinearity Advances in Differential Equations, 7 (9). pp. 1073-1100.

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Abstract

This article is devoted to the study of the long-time behavior of solutions of the following 4th order parabolic system in a bounded smooth domain Ω ⊂⊂ ℝn: b∂t u = -δx (aδxu - a∂tu - f(u) + g̃), (1) where u = (u1,., uk) is an unknown vector-valued function, a and b are given constant matrices such that a + a* > 0, b = b* > 0, α > 0 is a positive number, and f and g are given functions. Note that the nonlinearity f is not assumed to be subordinated to the Laplacian. The existence of a finite dimensional global attractor for system (1) is proved under some natural assumptions on the nonlinear term f.

Item Type: Article
Authors :
NameEmailORCID
Efendiev, MAUNSPECIFIEDUNSPECIFIED
Gajewski, HUNSPECIFIEDUNSPECIFIED
Zelik, Ss.zelik@surrey.ac.ukUNSPECIFIED
Date : 1 December 2002
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 13:13
Last Modified : 17 May 2017 15:09
URI: http://epubs.surrey.ac.uk/id/eprint/838398

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