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Guo, C.X. and Mu, C.L. (2007) Exponential Attractors for a Non-Classical Diffusion Equation. Journal of Chongqing University (Natural Science Edition), 30, 87-90.

has been cited by the following article:

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

  AUTHORS: Guoguang Lin, Lujiao Yang

  KEYWORDS: Kirchhoff-Type Equation, Spectral Interval Condition, A Family of the Exponential Attractors, A Family of the Inertial Manifolds

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.9 No.10, September 30, 2021

  ABSTRACT: In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Kirchhoff stress term and nonlinear term, the existence of exponential attractor is obtained by proving the discrete squeezing property of the equation, then according to Hadamard’s graph transformation method, the spectral interval condition is proved to be true, therefore, the existence of a family of the inertial manifolds for the equation is obtained.