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Wu, J.Z. and Lin, G.G. (2010) The Inertial Manifold of The Two-Dimensional Strong Damping Boussinesq Equation. Journal of Yunnan University, 32, 119-124.

has been cited by the following article:

• TITLE: The Inertial Manifold for Class Kirchhoff-Type Equations with Strongly Damped Terms and Source Terms

  AUTHORS: Guoguang Lin, Xiangshuang Xia

  KEYWORDS: Inertial Manifold, Hadamard’s Graph Transformation Method, Lipschitz Continuous, Spectral Gap Condition

  JOURNAL NAME: Applied Mathematics, Vol.9 No.6, June 29, 2018

  ABSTRACT: In this paper, we study the inertial manifolds for a class of the Kirchhoff-type equations with strongly damped terms and source terms. The inertial manifold is a finite dimensional invariant smooth manifold that contains the global attractor, attracting the solution orbits by the exponential rate. Under appropriate assumptions, we firstly exert the Hadamard’s graph transformation method to structure a graph norm of a Lipschitz continuous function, and then we prove the existence of the inertial manifold by showing that the spectral gap condition is true.