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Ciprian, F., George, R.S. and Roger, T. (1998) Inertial Manifolds for Nonlinear Evolutionary Equations. Journal of Differential Equations, 73, 309-353.
https://doi.org/10.1016/0022-0396(88)90110-6

has been cited by the following article:

• TITLE: A Family of Exponential Attractors and Inertial Manifolds for a Class of Higher Order Kirchhoff Equations

  AUTHORS: Guoguang Lin, Yingguo Wang

  KEYWORDS: Kirchhoff Equation, Lipschitz Property, Squeezing Property, a Family of the Exponential Attractors, a Family of Inertial Manifolds

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.3, March 25, 2022

  ABSTRACT: In this paper, the global dynamics of a class of higher order nonlinear Kirchhoff equations under n-dimensional conditions is studied. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup associated with the initial boundary value problem are proved, and the existence of a family of exponential attractors is obtained. Then, by constructing the corresponding graph norm, the condition of a spectral interval is established when N is sufficiently large. Finally, the existence of the family of inertial manifolds is obtained.