Cahn-Hilliard方程的动态分歧
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摘要
利用线性全连续场的谱理论,中心流形约化方法与非线性耗散系统吸引子分歧理论,研究了Cahn-Hilliard方程的动态分歧,给出了发生分歧的条件及临界点,并给出了在Neumann边界条件下,方程分歧出的稳定奇点吸引子和鞍点的表达式.
With the guidance of spectrum theory of the linear completely continuous fields, center manifolds reduction method and transition theory of nonlinear dissipative system, this paper invests dynamic bifurcation of Cahn-Hilliard equation. The conditions of the divergence, its critical point and the expression of the stable singularity attractor and saddle points of the equation with Neumann boundary condition are given in this paper.
With the guidance of spectrum theory of the linear completely continuous fields, center manifolds reduction method and transition theory of nonlinear dissipative system, this paper invests dynamic bifurcation of Cahn-Hilliard equation. The conditions of the divergence, its critical point and the expression of the stable singularity attractor and saddle points of the equation with Neumann boundary condition are given in this paper.
引文
[1]马天,汪守宏.非线性演化方程的稳定性与分歧[M].北京:科学出版社, 2007.
[2] Ma T, Wang S H. Bifurcation Theory and Applications[M]. Beijing:World Scientific Publishing Co., 2005.
[3] Cahn J W, Hilliard J E. Free energy of a nonuniform system I interfacial free energy[J]. Journal of Chemical Physics, 1958,28(2):258-267.
[4] Song Haitao, Wu Hongqing. Pullback attractors of nonauton-omous reaction diffusion equations[J].Journal of Mathematical Analysis and Applications, 2007,325(2):1200-1215.
[5]任丽,李晓军.非自治反应扩散方程的拉回D-吸引子[J].江南大学学报, 2014,13(2):237-242.
[6]马腾洋,姜金平.粘性Cahn-Hilliard方程的拉回D-吸引子[J].云南师范大学学报, 2016,36(5):33-37.
[7]罗宏,蒲志林,陈光淦.具有一般非线性项的Cahn-Hilliard方程的整体吸引子[J].四川师范大学学报,2002,25(4):333-338.
[8]张强.一类带Neumann边界条件的Cahn-Hilliard方程的定态分歧[J].四川大学学报, 2011,48(3):529-533.
[9]王会超,武瑞丽,侯智博.一类具有扩散项SIR模型的动态分歧[J].四川师范大学学报, 2015,38(3):239-242.
[10]马天.偏微分方程理论与方法[M].北京:科学出版社, 2011.
[11]马天.从数学观点看物理世界[M].北京:科学出版社, 2012.
[12] Ma Tian, Wang Shouhong. Dynamic bifurcation of nonlinear evolution equations[J]. Chinese Annals Mathematics B, 2005,26(2):185-206.
[13] Amy N C, Lee A. Nonlinear aspects of the Cahn-Hilliard equation[J]. Physica D:Nonlinear Phenomena, 1984,10(3):277-298.
[14] Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics[M]. New York:Springer-Verlag, 1998.
[15]钟承奎,范先令,陈文塬.非线性泛函分析引论[M].兰州:兰州大学出版社, 1998.
[2] Ma T, Wang S H. Bifurcation Theory and Applications[M]. Beijing:World Scientific Publishing Co., 2005.
[3] Cahn J W, Hilliard J E. Free energy of a nonuniform system I interfacial free energy[J]. Journal of Chemical Physics, 1958,28(2):258-267.
[4] Song Haitao, Wu Hongqing. Pullback attractors of nonauton-omous reaction diffusion equations[J].Journal of Mathematical Analysis and Applications, 2007,325(2):1200-1215.
[5]任丽,李晓军.非自治反应扩散方程的拉回D-吸引子[J].江南大学学报, 2014,13(2):237-242.
[6]马腾洋,姜金平.粘性Cahn-Hilliard方程的拉回D-吸引子[J].云南师范大学学报, 2016,36(5):33-37.
[7]罗宏,蒲志林,陈光淦.具有一般非线性项的Cahn-Hilliard方程的整体吸引子[J].四川师范大学学报,2002,25(4):333-338.
[8]张强.一类带Neumann边界条件的Cahn-Hilliard方程的定态分歧[J].四川大学学报, 2011,48(3):529-533.
[9]王会超,武瑞丽,侯智博.一类具有扩散项SIR模型的动态分歧[J].四川师范大学学报, 2015,38(3):239-242.
[10]马天.偏微分方程理论与方法[M].北京:科学出版社, 2011.
[11]马天.从数学观点看物理世界[M].北京:科学出版社, 2012.
[12] Ma Tian, Wang Shouhong. Dynamic bifurcation of nonlinear evolution equations[J]. Chinese Annals Mathematics B, 2005,26(2):185-206.
[13] Amy N C, Lee A. Nonlinear aspects of the Cahn-Hilliard equation[J]. Physica D:Nonlinear Phenomena, 1984,10(3):277-298.
[14] Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics[M]. New York:Springer-Verlag, 1998.
[15]钟承奎,范先令,陈文塬.非线性泛函分析引论[M].兰州:兰州大学出版社, 1998.