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.
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.
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.
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. https://doi.org/10.1016/j.na.2004.03.023