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Messaoudi, S.A. and Houari, B.S. (2007) A Blow-Up Result for a Higher-Order Nonlinear Kirchhoff-Type Hyperbolic Equation. Applied Mathematics Letters, 20, 866-871.
https://doi.org/10.1016/j.aml.2006.08.018

has been cited by the following article:

• TITLE: The Family of Exponential Attractors and Inertial Manifolds for a Generalized Nonlinear Kirchhoff Equations

  AUTHORS: Guoguang Lin, Xiaomei Liu

  KEYWORDS: A Family of the Exponential Attractors, Inertial Fractal Set, Squeezing Property, Spectral Gap Condition, A Family of the Inertial Manifolds

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.1, January 24, 2022

  ABSTRACT: In this paper, we study the long-time behavior of a class of generalized nonlinear Kichhoff equation under the condition of n dimension. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup related to the initial-boundary value problem are proved, and then the existence of its exponential attractor is obtained. By extending the space E0 to Ek, a family of the exponential attractors of the initial-boundary value problem is obtained. In the second part, we consider the long-time behavior for a system of generalized Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectrum interval condition.