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数学与物理
应用数学进展
Vol. 10 No. 7 (July 2021)
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非自治Boissonade系统解的长时间性态刻画
Long Time Characterization of Solutions of Nonautonomous Boissonade Systems
DOI:
10.12677/AAM.2021.107256
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被引量
下载: 273
浏览: 355
作者:
崔振琼
*
,
杨成明
:上海师范大学,上海
关键词:
非自治动力系统
;
一致吸引子
;
连续过程
;
全局吸引子
;
平移有界
;
Non-Autonomous Dynamical Systems
;
Uniform Attractor
;
Continuous Process
;
Global Attractor
;
Translation Bounded
摘要:
这篇论文主要包括以下两个方面: 首先证明了自治Boissonade 系统弱解的唯一性. 因为自 治Boissonade系统的二次项是uv而不是u
2
, 所以在证明弱解的唯一性时与一般方法有所差别, 因 此, 本文给出了证明弱解唯一性的具体方法. 最后, 根据一致吸引子存在的充分必要条件证明了非 自治Boissonade 系统的一致吸引子在E 中的存在性。
Abstract:
This paper mainly includes the following two aspects: Firstly, we prove the uniqueness of weak solution of autonomous Boissonade system. Because the quadratic term of the autonomous Boissonade system is uv instead of u
2
, it is different from the general method when proving the uniqueness of weak solution. Therefore, this paper gives a specific method to prove the uniqueness of weak solution. Finally, according to the sufficient and necessary conditions for the existence of uniform attractor, the existence of uniform attractor in E of non-autonomous Boissonade system is proved.
文章引用:
崔振琼, 杨成明. 非自治Boissonade系统解的长时间性态刻画[J]. 应用数学进展, 2021, 10(7): 2442-2456.
https://doi.org/10.12677/AAM.2021.107256
参考文献
[1]
Robinson, J.C. and Pierre, C. (2003) Infinite-Dimensional Dynamical Systems: An Introduc- tion to Dissipative Parabolic PDEs and the Theory of Global Attractors. Cambridge Texts in Applied Mathematics. Applied Mechanics Reviews, 56, B54-B55.
https://doi.org/10.1115/1.1579456
[2]
Haraux, A. (1991) Syst`emes dynamiques dissipatifs et applications. In: Syst`emes Dynamiques Dissipatifs et Applications, Masson, Paris.
[3]
Chepyzhov, V.V. and Vishik, M.I. (2002) Attractors for Equations of Mathematical Physics. Vol. 49, American Mathematical Society, Providence, RI.
https://doi.org/10.1090/coll/049
[4]
Ma, Q.F., Wang, S.H. and Zhong, C.K. (2002) Necessary and Sufficient Conditions for the Ex-istence of Global Attractors for Semigroups and Applications. Indiana University Mathematics Journal, 51, 1541-1559.
[5]
Lu, S.S., Wu, H.Q. and Zhong, C.K. (2005) Attractors for Nonautonomous 2D Navier-Stokes Equations with Normal External Forces. Discrete and Continuous Dynamical Systems, 13, 701-719.
https://doi.org/10.3934/dcds.2005.13.701
[6]
Sell, G.R. and You, Y. (2002) Dynamics of Evolutionary Equations. Springer, New York.
[7]
Tu, J.Y. (2015) Global Attractors and Robustness of the Boissonade System. Journal of Dy- namics and Differential Equations, 27, 187-211.
https://doi.org/10.1007/s10884-014-9396-8
[8]
Song, H.T., Ma, S. and Zhong, C.K. (2009) Attractors of Non-Autonomous Reaction-Diffusion Equations. Nonlinearity, 22, 667-681.
https://doi.org/10.1088/0951-7715/22/3/008
[9]
周盛凡, 赵敏, 向晓林. 非自治Boissonade系统的拉固和一致指数吸寻子[J]. 中国科学(数学), 2017, 47(12): 1891-1906.
https://doi.org/10.1360/N012017-00062
[10]
Song, H.T. and Zhong, C.K. (2008) Attractors of Non-Autonomous Reaction-Diffusion Equa- tions in Lp. Nonlinear Analysis: Theory, Methods and Applications, 68, 1890-1897.
https://doi.org/10.1016/j.na.2007.01.059
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