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Global attractor for the Cahn-Hilliard system with fast growing nonlinearity. (English) Zbl 0912.35029
It is studied the system of Cahn-Hilliard equations: $$u_t-\Delta (-\Gamma\Delta u=\nabla_u\varphi(u))= 0\quad\text{on }\bbfR_+\times\Omega,$$ supplied with homogeneous boundary conditions and initial conditions. The authors prove that the system possess a global attractor.

35B40Asymptotic behavior of solutions of PDE
35K50Systems of parabolic equations, boundary value problems (MSC2000)
35-99Partial differential equations (PDE) (MSC2000)
37C70Attractors and repellers, topological structure
Full Text: DOI
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[2] Cholewa, J. W.; Dlotko, T.: Global attractor of the Cahn--Hilliard system. Bull. austral. Math. soc. 49, 202-277 (1994) · Zbl 0803.35013
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[6] D. J. Eyre, System of Cahn--Hilliard equations, University of Minnesota, 1992 · Zbl 0853.73060
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[8] Henry, D.: Geometric theory of semilinear parabolic equations. (1981) · Zbl 0456.35001
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[10] Rodriguez-Bernal, A.: CDSNS report. (1991)
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[12] Temam, R.: Navier--Stokes equations, theory and numerical analysis. (1984) · Zbl 0568.35002