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Asymptotic limits of viscous Cahn--Hilliard equation with homogeneous Dirichlet boundary condition 1 1 Introduction 1 2 Main results 3 3 Proof of Theorem 2.2 9 3.1 A priori estimates independent of γ 9 3.2 Asymptotic limit as γ→0 12 4 Proof of Theorem 2.3 14 4.1 A priori estimates independent of β 14 4.2 Asymptotic limit as β→0 16 5 Proofs of Theorem 2.5 and Corollary 2.6 17 5.1 A priori estimates independent of α 17 5.2 Asymptotic limit as α→0 20 5.3 Proof of Corollary 2.6 22 Acknowledgments 23 References 23

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