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Matsuyama, T. and Ikehata, R. (1996) On Global Solutions and Energy Decay for the Wave Equations of Kirchhoff Type with Nonlinear Damping Terms. Journal of Mathematical Analysis and Applications, 204, 729-753.
https://doi.org/10.1006/jmaa.1996.0464

has been cited by the following article:

• TITLE: A Family of Global Attractors for a Class of Generalized Kirchhoff-Beam Equations

  AUTHORS: Yuhuai Liao, Guoguang Lin, Jie Liu

  KEYWORDS: High-Order Kirchhoff-Beam Equation, Galerkin’s Method, Family of Global Attractors, The Hausdorff Dimension

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.3, March 30, 2022

  ABSTRACT: The initial boundary value problem for a class of high-order Beam equations with quasilinear and strongly damped terms is studied. Firstly, the existence and uniqueness of the global solution of the equation are proved by prior estimation and Galerkin finite element method. Then the bounded absorption set is obtained by prior estimation, and the family of global attractors for the high-order Kirchhoff-Beam equation is obtained. The Frechet differentiability of the solution semigroup is proved after the linearization of the equation, and the decay of the volume element of the linearization problem is further proved. Finally, the Hausdorff dimension and Fractal dimension of the family of global attractors are proved to be finite.