粘性Cahn-Hilliard方程解的渐近性
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摘要
利用一种新的方法研究粘性Cahn-Hilliard方程的一致吸引子。首先讨论过程的一致吸收集;其次利用压缩函数证明过程的一致渐近紧性,进而得到了粘性Cahn-Hilliard方程一致吸引子的存在性。
The uniform attractor of viscous Cahn-Hilliard equation was studied by using a new method. Firstly,the uniform absoring set of the process is discussed. Secondly,using contractive functions,the uniformly asymptotical compactness of the process is proved and then the existence of the uniform attractor of viscous Cahn-Hilliard equation is obtained.
The uniform attractor of viscous Cahn-Hilliard equation was studied by using a new method. Firstly,the uniform absoring set of the process is discussed. Secondly,using contractive functions,the uniformly asymptotical compactness of the process is proved and then the existence of the uniform attractor of viscous Cahn-Hilliard equation is obtained.
引文
[1]Efendiev M,Miranville A,Zelik S. Exponential attractors for a singularly perturbed Cahn-Hilliard system[J]. Math.Nachr.,2004,272:11-31.
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[3]Miranville A,Zelik S. Robust exponential attractors for Cahn-Hilliard type equations with singular potentials[J]. Math.Methods Appl. Sci.,2004,27:545-582.
[4]Novick-Cohen A. The Cahn-Hilliard equation:mathematical and modeling perspectives[J]. Adv. Math. Sci. Appl.,1998,8:965-985.
[5]Rybka P,Hoffmann K H. Convergence of solutions to Cahn-Hilliard equation[J]. Comm. Partial Differential Equations,1999,24:1055-1077.
[6]Cahn J W. On spinodal decomposition[J]. Acta Metall,1961,9(3):795-801.
[7]Cahn J W,Hilliard J E. Free energy of a non-uniform system I. Interfacial free energy[J]. J Chen Phys,1958,2(2):258-267.
[8]Dlotko T. Global attractor for the Cahn-Hilliard equation in H2 and H3[J]. J Differential Equations,1994,113(2):381-393.
[9]王素云,李德生,张艳红. Cahn-Hilliard方程强解的全局吸引子[J].兰州大学学报,2005(5):139-142.
[10]董超雨,姜金平,张晓明.非自治Cahn-Hilliard方程的一致吸引子[J].郑州大学学报(理学版),2014,46(2):21-23+30.
[11]王艳,姜金平,张凤,等.有界区域上自治Cahn-Hilliard方程的指数吸引子[J].贵州大学学报(自然科学版),2016,33(6):14-15+32.
[12]安丽坤.粘性Cahn-Hilliard方程的大范围动力学(英文)[J].兰州大学学报,2000(5):17-23.
[13]刘长春.粘性Cahn-Hilliard方程的径向解[J].工程数学学报,2004(2):233-237.
[14]董超雨,姜金平,张晓明.粘性Cahn-Hilliard方程在L2空间中的全局吸引子[J].贵州大学学报(自然科学版),2013,30(4):7-8+35.
[15]董超雨,姜金平,张晓明.粘性Cahn-Hilliard方程全局吸引子的存在性[J].湖北大学学报(自然科学版),2014,36(4):385-388.
[16]董超雨,姜金平,张晓明.粘性Cahn-Hilliard方程全局吸引子的维数估计[J].延安大学学报(自然科学版),2014,33(3):15-16.
[17]董超雨,姜金平,张晓明.粘性Cahn-Hilliard方程的一致吸引子[J].贵州大学学报(自然科学版),2014,31(5):12-14.
[18]Teman R. Infinite Dimensional Dynamical Systems in Mechanics and Physics[M]. New York:Springerverlag,1988.
[19]Song Haitao,Wu Hongqing. Pullback attractors of nonautonomous reaction-diffusion equations[J]. Journal of Mathematical Analysis and Application,2007,325(2):1200-1215.
[20]Chepyzhov V V and Vishik M I. Attractors for Equations of Mathematical Physics,Providence[M]. RI:American Mathematical Society,2001.
[2]Elliott C M,Zheng S. On the Cahn-Hilliard equation[J].Arch. Rational Mech. Anal.,1986,96:339-357.
[3]Miranville A,Zelik S. Robust exponential attractors for Cahn-Hilliard type equations with singular potentials[J]. Math.Methods Appl. Sci.,2004,27:545-582.
[4]Novick-Cohen A. The Cahn-Hilliard equation:mathematical and modeling perspectives[J]. Adv. Math. Sci. Appl.,1998,8:965-985.
[5]Rybka P,Hoffmann K H. Convergence of solutions to Cahn-Hilliard equation[J]. Comm. Partial Differential Equations,1999,24:1055-1077.
[6]Cahn J W. On spinodal decomposition[J]. Acta Metall,1961,9(3):795-801.
[7]Cahn J W,Hilliard J E. Free energy of a non-uniform system I. Interfacial free energy[J]. J Chen Phys,1958,2(2):258-267.
[8]Dlotko T. Global attractor for the Cahn-Hilliard equation in H2 and H3[J]. J Differential Equations,1994,113(2):381-393.
[9]王素云,李德生,张艳红. Cahn-Hilliard方程强解的全局吸引子[J].兰州大学学报,2005(5):139-142.
[10]董超雨,姜金平,张晓明.非自治Cahn-Hilliard方程的一致吸引子[J].郑州大学学报(理学版),2014,46(2):21-23+30.
[11]王艳,姜金平,张凤,等.有界区域上自治Cahn-Hilliard方程的指数吸引子[J].贵州大学学报(自然科学版),2016,33(6):14-15+32.
[12]安丽坤.粘性Cahn-Hilliard方程的大范围动力学(英文)[J].兰州大学学报,2000(5):17-23.
[13]刘长春.粘性Cahn-Hilliard方程的径向解[J].工程数学学报,2004(2):233-237.
[14]董超雨,姜金平,张晓明.粘性Cahn-Hilliard方程在L2空间中的全局吸引子[J].贵州大学学报(自然科学版),2013,30(4):7-8+35.
[15]董超雨,姜金平,张晓明.粘性Cahn-Hilliard方程全局吸引子的存在性[J].湖北大学学报(自然科学版),2014,36(4):385-388.
[16]董超雨,姜金平,张晓明.粘性Cahn-Hilliard方程全局吸引子的维数估计[J].延安大学学报(自然科学版),2014,33(3):15-16.
[17]董超雨,姜金平,张晓明.粘性Cahn-Hilliard方程的一致吸引子[J].贵州大学学报(自然科学版),2014,31(5):12-14.
[18]Teman R. Infinite Dimensional Dynamical Systems in Mechanics and Physics[M]. New York:Springerverlag,1988.
[19]Song Haitao,Wu Hongqing. Pullback attractors of nonautonomous reaction-diffusion equations[J]. Journal of Mathematical Analysis and Application,2007,325(2):1200-1215.
[20]Chepyzhov V V and Vishik M I. Attractors for Equations of Mathematical Physics,Providence[M]. RI:American Mathematical Society,2001.