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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.
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Keywords:
- nonlinear thermal effect /
- Sine-Gordon equation /
- global attractor
[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 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 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 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 60 070205]
[12] Wang D X, Zhang J W 2010 J. Math. Anal. Appl. 363 468
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[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 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 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 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 60 070205]
[12] Wang D X, Zhang J W 2010 J. Math. Anal. Appl. 363 468
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