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In this paper, solving the following forms of fourth order parabolic Cahn-Hilliard equation at the beginning of Boundary Value Problems pseudo-spectral method and the spectral method where u = u (x, t) for the mutual diffusion of the two substances , one of density , γ gt ; 0 is the mobility . φ (u) ≡ H '(u), H (u) is a typical shuangjing potential function : this article assumes that γ1 = 0, the first time this paper gives a solution when γ is constant with constant mobility Cahn-Hilliard equation variational problem , and then were used pseudo-spectral method and the spectral method for spatial variables χ made ??discrete approximation and solved numerically , thus verifying the existing theoretical solution of this equation is semi- discrete problem nature , that is, when he γ2 gt; 0时unique solution exists , as well as γ2 lt; 0 semi-discrete problem may occur bursting phenomenon . then we use pseudo-spectral method to solve when γ = m (x, t) when with defined variable mobility Cahn-Hilliard equation , and find numerical approximate solution.
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