Back
 IJMNTA  Vol.5 No.1 , March 2016
Global Attractors for a Class of Generalized Nonlinear Kirchhoff-Sine-Gordon Equation
Abstract: In this paper, we consider a class of generalized nonlinear Kirchhoff-Sine-Gordon equation . By a priori estimation, we first prove the existence and uniqueness of solutions to the initial boundary value conditions, and then we study the global attractors of the equation.
Cite this paper: Lou, R. , Lv, P. and Lin, G. (2016) Global Attractors for a Class of Generalized Nonlinear Kirchhoff-Sine-Gordon Equation. International Journal of Modern Nonlinear Theory and Application, 5, 73-81. doi: 10.4236/ijmnta.2016.51008.
References

[1]   Kirchhof, G. (1883) Vorlesungen fiber Mechanik. Teubner, Stuttgarty.

[2]   Masamro, H. and Yoshio, Y. (1991) On Some Nonlinear Wave Equations 2: Global Existence and Energy Decay of Solutions. J. Fac. Sci. Univ. Tokyo. Sect. IA, Math., 38, 239-250.

[3]   Josephson, B.D. (1962) Possible New Effects in Superconductive Tunneling. Physics Letters, 1, 251-253.
http://dx.doi.org/10.1016/0031-9163(62)91369-0

[4]   Zhu, Z.W. and Lu, Y. (2000) The Existence and Uniqueness of Solution for Generalized Sine-Gordon Equation. Chinese Quarterly Journal of Mathematics, 15, 71-77.

[5]   Li, Q.X. and Zhong, T. (2002) Existence of Global Solutions for Kirchhoff Type Equations with Dissipation and Damping Terms. Journal of Xiamen University: Natural Science Edition, 41, 419-422.

[6]   Silva, M.A.J. and Ma, T.F. (2013) Long-Time Dynamics for a Class of Kirchhoff Models with Memory. Journal of Mathematical Physics, 54, Article ID: 021505.

[7]   Zhang, J.W., Wang, D.X. and Wu, R.H. (2008) Global Solutions for a Class of Generalized Strongly Damped Sine-Gordon Equation. Journal of Mathematical Physics, 57, 2021-2025.

[8]   Guo, L., Yuan, Z.Q. and Lin, G.G. (2014) The Global Attractors for a Nonlinear Viscoelastic Wave Equation with Strong Damping and Linear Damping and Source Terms. International Journal of Modern Nonlinear Theory and Application, 4, 142-152.
http://dx.doi.org/10.4236/ijmnta.2015.42010

[9]   Teman, R. (1988) Infiniter-Dimensional Dynamical Systems in Mechanics and Physics. Springer-Verlag, New York, 15-26.
http://dx.doi.org/10.1007/978-1-4684-0313-8_2

[10]   Ma, Q.F., Wang, S.H. and Zhong, C.K. (2002) Necessary and Sufficient Congitions for the Existence of Global Attractors for Semigroup and Applications. Indiana University Mathematics Journal, 51, 1541-1559.
http://dx.doi.org/10.1512/iumj.2002.51.2255

[11]   Ma, Q.Z., Sun, C.Y. and Zhong, C.K. (2007) The Existence of Strong Global Attractors for Nonlinear Beam Equations. Journal of Mathematical Physics, 27A, 941-948.

[12]   Lin, G.G. (2011) Nonlinear Evolution Equation. Yunnan University Press, 12.

 
 
Top