粘性Cahn-Hilliard方程的可解性
Solvability of Viscous Cahn-Hilliard Equation
摘要: 本文研究粘性Cahn-Hilliard方程的可解性问题。通过构造扇形算子并且利用文献中的方法证明了粘性Cahn-Hilliard方程局部解的存在性和整体解的存在性。同时，考虑带有非线性的粘性Cahn-Hilliard方程，研究其可解性问题。
Abstract: In this paper, we study the solvability of the viscous Cahn-Hilliard equation. By constructing sectorial operators and empolying the method in reference, the existence of local solutions and global solutions for viscous Cahn-Hilliard equation are proved. At the same time, the existence of solutions for the viscous Cahn-Hilliard equation with nonlinear term is studied.
文章引用：黄梅, 蒲志林, 段芳. 粘性Cahn-Hilliard方程的可解性[J]. 应用数学进展, 2020, 9(10): 1734-1742. https://doi.org/10.12677/AAM.2020.910200

参考文献

[1] Novick-Cohen, A. (1988) On the Viscous Cahn-Hilliard Equation, Material Instabilities in Continuum Mechanics and Related Mathematical Problems. Clarendon Press, Oxford, 329-342.
[2] Dlotko, T., Kania, M.B. and Sun, C.Y. (2012) Analysis of the Viscous Cahn-Hilliard Equation in RN. Journal of Differential Equation, 252, 2771-2791. [Google Scholar] [CrossRef] 
[3] Bui, L.T.T., Dao, A.N. and Díaz, J.L. (2017) Critical Case for the Viscous Cahn-Hilliard Equation. Electronic Journal of Differential Equations, 176, 1-8.
[4] Choo, S.M. and Chung, S.K. (2003) Asymtotic Behaviour of the Viscous Cahn-Hilliard Equation. Journal of Applied Mathematics and Computing, 11, 143-154. [Google Scholar] [CrossRef] 
[5] Rossi, R. (2007) Global Attractor for the Weak Solutions of a Class of Viscous Cahn-Hilliard Equations, Dissipative Phase Transitions. Series on Advances in Mathematics for Applied Sciences, 71, 247-268. [Google Scholar] [CrossRef] 
[6] Carvalho, A.N. and Dlotko, T. (2008) Dynamics of the Viscous Cahn-Hilliard Equation. Journal of Mathematical Analysis and Applications, 344, 703-725. [Google Scholar] [CrossRef] 
[7] Cholewa, J.W. and Dlotko, T. (2010) Dynamics of the Modified Viscous Cahn-HillIiard Equation in RN. Topological Methods in Nonlinear Analysis, 35, 277-294.
[8] Elliott, C.M. and Stuart, A.M. (1996) Viscous Cahn-Hilliard Equation II. Analysis. Journal of Differential Equations, 128, 387-414. [Google Scholar] [CrossRef] 
[9] Choo, S.M. and Chung, S.K. (2004) A Conservative Nonlinear Difference Scheme for the Viscous Cahn-Hilliard Equation. Journal of Applied Mathematics and Computing, 16, 53-68. [Google Scholar] [CrossRef] 
[10] Cholewa, J.W. and Dlotko, T. (2000) Global Attractors in Abstract Parabolic Problems. Cambridge University Press, Cambridge. [Google Scholar] [CrossRef] 
[11] 任永华. 粘性Cahn-Hilliard方程的整体吸引子[J]. 应用数学进展, 2016, 5(4): 818-822.
[12] Pazy, A. (1983) Semigroups of Linear Operator and Applications to Partial Differential Equation. Spring Verlag, New York. [Google Scholar] [CrossRef] 

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