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- W1982528487 abstract "This paper deals with the Cahn–Hilliard equation $$psi_t=Delta mu, quad mu = -Delta psi-psi+psi^3,quad (t, x)in Jtimes Omega,$$ subject to the boundary conditions $$frac{1}{Gamma_s}psi_t = sigma_s Delta_{||} psi-partial_nu psi - g_s psi +h,quad partial_nu mu=0,$$ and the initial condition ψ(0,x) = ψ0(x) where J = (0,∞), and Ω ⊂ ℝ n is a bounded domain with smooth boundary Γ = ∂ G, n≤ 3, and Γ s ,σ s ,g s > 0, h are constants. This problem has already been considered in the recent paper of R. Racke and S. Zheng (The Cahn–Hilliard equation with dynamic boundary conditions. Adv. Diff. Eq. 8, 83–110, 2003), where global existence and uniqueness were obtained. In this paper we first obtain results on the maximal L p -regularity of the solution. We then study the asymptotic behavior of the solution of this problem and prove the existence of a global attractor." @default.
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- W1982528487 date "2006-01-03" @default.
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- W1982528487 title "Maximal regularity and asymptotic behavior of solutions for the Cahn–Hilliard equation with dynamic boundary conditions" @default.
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- W1982528487 doi "https://doi.org/10.1007/s10231-005-0175-3" @default.
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