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In this paper, we prove the existence of the global attractor for strongly damped nonlinear thermoelastic coupled rod equation with the initial boundary value, and make the dimension estimate of the global attractor, according to the operator semigroups theory.
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Keywords:
- thermoelastic coupled rod system /
- strongly damped /
- nonlinear /
- global attractor
[1] Temam R 1988 Infinite-Dimensional Dynamical Systems in Mechanics and Physics (NewYork: Springer)
[2] Zhang M X, Liu Q P, Wang J Wu K 2008 Chin. Phys. B 17 10
[3] Chen Y, Fan E G 2007 Chin. Phys. 16 0006
[4] Liu Y 2009 Acta Phys. Sin. 58 7452 (in Chinese)[刘 煜 2009 58 7452]
[5] Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 6214(in Chinese)[套格图桑、斯仁道尔吉 2006 55 6214]
[6] Shi Y R, Yang H J 2010 Acta Phys. Sin. 59 67 (in Chinese)[石玉仁、杨红娟 2010 59 67]
[7] Wang D X, Zhang J W 2010 J. Math. Anal. Appl. 363 468
[8] Zhang J W, Rong X L, Wu R H 2009 Chin. Phys. B 18 3693
[9] 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]
[10] Wang D X, Zhang J W, Wu R H 2008 Acta Phys. Sin. 57 6741
[11] Zhou S F 1999 J. Math. Anal. Appl. 233 102
[12] Chen S Q, Zhou S F, Li H Y 2008 Comm.On.Appl.Math.And.Comput. 22 14
[13] Wu Y F 2008 MS Thesis (South China University of Technology) (in Chinese)[硕士论文(广州:华南理工大学)]
[14] Pazy A 1983 Semigroups of Linear Operators and Applications to Partial Differential Equations (New York:Springer) p183
[15] Massant P 1983 J. Differential Equations 48 334
[16] Hale J K 1988 Asymptotic Behavior of Dissipative Systems (Providence :Rhode Island) p1
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[1] Temam R 1988 Infinite-Dimensional Dynamical Systems in Mechanics and Physics (NewYork: Springer)
[2] Zhang M X, Liu Q P, Wang J Wu K 2008 Chin. Phys. B 17 10
[3] Chen Y, Fan E G 2007 Chin. Phys. 16 0006
[4] Liu Y 2009 Acta Phys. Sin. 58 7452 (in Chinese)[刘 煜 2009 58 7452]
[5] Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 6214(in Chinese)[套格图桑、斯仁道尔吉 2006 55 6214]
[6] Shi Y R, Yang H J 2010 Acta Phys. Sin. 59 67 (in Chinese)[石玉仁、杨红娟 2010 59 67]
[7] Wang D X, Zhang J W 2010 J. Math. Anal. Appl. 363 468
[8] Zhang J W, Rong X L, Wu R H 2009 Chin. Phys. B 18 3693
[9] 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]
[10] Wang D X, Zhang J W, Wu R H 2008 Acta Phys. Sin. 57 6741
[11] Zhou S F 1999 J. Math. Anal. Appl. 233 102
[12] Chen S Q, Zhou S F, Li H Y 2008 Comm.On.Appl.Math.And.Comput. 22 14
[13] Wu Y F 2008 MS Thesis (South China University of Technology) (in Chinese)[硕士论文(广州:华南理工大学)]
[14] Pazy A 1983 Semigroups of Linear Operators and Applications to Partial Differential Equations (New York:Springer) p183
[15] Massant P 1983 J. Differential Equations 48 334
[16] Hale J K 1988 Asymptotic Behavior of Dissipative Systems (Providence :Rhode Island) p1
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