Zhang, S.L., Zhang, J.W. and Wang, H.Y. (2020) Global Attractors for Kirchhoff Wave Equation with Nonlinear Damping and Memory. Boundary Value Problems, 2020, Article No. 116.
https://doi.org/10.1186/s13661-020-01413-5

has been cited by the following article:

• TITLE: The Dynamic Behavior of a Class of Kirchhoff Equations with High Order Strong Damping

  AUTHORS: Guoguang Lin, Chunmeng Zhou

  KEYWORDS: Kirchhoff Equation, Prior Estimate, The Existence and Uniqueness of the Solution, Family of Global Attractor, Dimension Estimation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.9 No.5, May 26, 2021

  ABSTRACT: In this paper, we study the long time behavior of a class of Kirchhoff equations with high order strong dissipative terms. On the basis of the proper hypothesis of rigid term and nonlinear term of Kirchhoff equation, firstly, we evaluate the equation via prior estimate in the space E0 and Ek, and verify the existence and uniqueness of the solution of the equation by using Galerkin’s method. Then, we obtain the bounded absorptive set B0k on the basis of the prior estimate. Moreover, by using the Rellich-Kondrachov Compact Embedding theorem, we prove that the solution semigroup S(t) of the equation has the family of the global attractor Ak in space Ek. Finally, we prove that the solution semigroup S(t) is Frechet differentiable on Ek via linearizing the equation. Furthermore, we can obtain the finite Hausdorff dimension and Fractal dimension of the family of the global attractor Ak.