All Title Author
Keywords Abstract

The Inertial Manifolds for a Class of Higher-Order Coupled Kirchhoff-Type Equations

DOI: 10.4236/jamp.2018.65091, PP. 1055-1064

Keywords: Higher-Order Coupled Kirchhoff-Type Equations, Inertial Manifold, Hadamard’s Graph, Spectral Gap Condition

Full-Text   Cite this paper   Add to My Lib


In this paper, we mainly deal with a class of higher-order coupled Kirch-hoff-type equations. At first, we take advantage of Hadamard’s graph to get the equivalent form of the original equations. Then, the inertial manifolds are proved by using spectral gap condition. The main result we gained is that the inertial manifolds are established under the proper assumptions of M(s) and gi(u,v), i=1, 2.


[1]  Wu, J.Z. and Lin, G.G. (2010) An Inertial Manifold of the Two-Dimensional Strongly Damped Boussinesq Equation. Journal of Yunnan University (Natural Science Edition), 32, 119-224.
[2]  Xu, G.G., Wang, L.B. and Lin, G.G. (2014) Inertial Manifold for a Class of the Retarded Nonlinear Wave Equations. Mathematica Applicata, 27, 887-891.
[3]  Lou, R.J., Lv, P.H. and Lin, G.G. (2016) Exponential Attractors and Inertial Manifolds for a Class of Generalized Nonlinear Kirchhoff-Sine-Gordon Equation. Journal of Advances in Mathematics, 12, 6361-6375.
[4]  Chen, L., Wang, W. and Lin, G.G. (2016) Exponential Attractors and Inertial Manifolds for the Higher-Order Nonlinear Kirchhof-Type Equation. International Journal of Modern Communication Technologies & Research, 4, 6-12.
[5]  Lin, G.G. (2011) Nonlinear Evolution Equation. Yunnan University Press, Kunming.
[6]  Robinson, J.C. (2001) Infinite Dimensional Dynamical System. Cambridge University Press, London.
[7]  Zheng, S.M. and Milani, A. (2004) Exponential Attractors and Inertial Manifold for Singular Perturbations of the Cahn-Hilliard Equations. Nonlinear Analysis, 57, 843-877.
[8]  Tmam, R. (1988) Infinite Dimensional Dynamical Systems in Mechanics and Physics. Springer Verlag, New York.


comments powered by Disqus