非线性热弹耦合Sine-Gordon型系统的整体吸引子

张建文; 任永华; 吴润衡; 冯涛

doi:10.7498/aps.61.110404

摘要

研究受Peierls-Nabarro力作用的非线性热弹耦合Sine-Gordon型系统的动力行为.利用算子半群理论证明了在一定的初边界条件下系统存在连续解, 利用算子半群分解技巧构造了渐近紧的不变吸收集, 进而证明了系统存在整体吸引子.

关键词:

The dynamical behavior of a class of coupled system to the Sine-Gordon equations with the Peierls-Nabarro force is considered in this paper. First, the existence of the continuous solution is shown in the semi-group approach, under the certain initial-boundary value condition. Then, using the decomposing technique of semi-group, we construct the compact positively invariant sets, and the global attractor is proved.

Keywords:

作者及机构信息

1.
太原理工大学数学学院, 太原 030024;

2.
北方工业大学理学院, 北京 100041

基金项目: 国家自然科学基金(批准号: 11172194)、山西省自然科学基金(批准号: 2010011008) 和山西省青年科技研究基金(批准号: 2011021002-2) 资助的课题.

Authors and contacts

1.
College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China;

2.
College of Science, North China University of Technology, Beijing 100041, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10772131), the Natural Science Foundation of Shanxi Province, China (Grant No. 2010011008), and the Natural Science Foundation for Young Scientists of Shanxi Province, China (Grant No. 2011021002-2).

参考文献

[1]	Zhang J W, Wang D X, Wu R H 2008 Acta Phys. Sin. 57 2021 (in Chinese) [张建文, 王旦霞, 吴润衡 2008 物理学报 57 2021]
[2]	Kriener C F, Zimmer J 2009 Nonlinear Anal. 70 3146
[3]	Chen S Q, Zhou S F, Li H Y 2008 Commun. Appl. Math. Comput. 22 14 (in Chinese) [陈双全, 周盛凡, 李红艳 2008 应用数学与计算数学学报 22 14]
[4]	Hollowood T J, Miramontes J L 2011 J. High Energy Phys. 4 119
[5]	Luo K F, Jiang X L, Yang Y L 2008 Chin. Phys. B 17 2600
[6]	Alvaro H S 2010 Nonlinear Anal. 11 3930
[7]	Taogetusang, Sirendaoerji 2010 Acta Phys. Sin. 59 5194 (in Chinese) [套格图桑, 斯仁道尔吉 2010 物理学报 59 5194]
[8]	Ma L M, Wu Z M 2009 Chin. Phys. B 18 3099
[9]	Lü D Z, Cui Y Y, Liu C H, Zhang Y 2010 Acta Phys. Sin. 59 6793 (in Chinese) [吕大昭, 崔艳英, 刘长河, 张艳 2010 物理学报 59 6793]
[10]	Temam R 1988 Infinite-Dimensional Dynamical Systems in Mechanics and Physics (New York: Springer) pp1--648
[11]	Zhang J W, Li J F, Wu R H 2011 Acta Phys. Sin. 60 070205 (in Chinese) [张建文, 李金峰, 吴润衡 2011 物理学报 60 070205]
[12]	Wang D X, Zhang J W 2010 J. Math. Anal. Appl. 363 468

施引文献

[1]	Zhang J W, Wang D X, Wu R H 2008 Acta Phys. Sin. 57 2021 (in Chinese) [张建文, 王旦霞, 吴润衡 2008 物理学报 57 2021]
[2]	Kriener C F, Zimmer J 2009 Nonlinear Anal. 70 3146
[3]	Chen S Q, Zhou S F, Li H Y 2008 Commun. Appl. Math. Comput. 22 14 (in Chinese) [陈双全, 周盛凡, 李红艳 2008 应用数学与计算数学学报 22 14]
[4]	Hollowood T J, Miramontes J L 2011 J. High Energy Phys. 4 119
[5]	Luo K F, Jiang X L, Yang Y L 2008 Chin. Phys. B 17 2600
[6]	Alvaro H S 2010 Nonlinear Anal. 11 3930
[7]	Taogetusang, Sirendaoerji 2010 Acta Phys. Sin. 59 5194 (in Chinese) [套格图桑, 斯仁道尔吉 2010 物理学报 59 5194]
[8]	Ma L M, Wu Z M 2009 Chin. Phys. B 18 3099
[9]	Lü D Z, Cui Y Y, Liu C H, Zhang Y 2010 Acta Phys. Sin. 59 6793 (in Chinese) [吕大昭, 崔艳英, 刘长河, 张艳 2010 物理学报 59 6793]
[10]	Temam R 1988 Infinite-Dimensional Dynamical Systems in Mechanics and Physics (New York: Springer) pp1--648
[11]	Zhang J W, Li J F, Wu R H 2011 Acta Phys. Sin. 60 070205 (in Chinese) [张建文, 李金峰, 吴润衡 2011 物理学报 60 070205]
[12]	Wang D X, Zhang J W 2010 J. Math. Anal. Appl. 363 468

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