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has been cited by the following article:

• TITLE: Approximate Inertial Manifold for a Class of the Kirchhoff Wave Equations with Nonlinear Strongly Damped Terms

  AUTHORS: Chengfei Ai, Huixian Zhu, Guoguang Lin

  KEYWORDS: Kirchhoff Wave Equation, Global Attractor, The Smoothing Effect, The Regularity, Approximate Inertial Manifold

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.5 No.4, November 29, 2016

  ABSTRACT: This paper is devoted to the long time behavior of the solution to the initial boundary value problems for a class of the Kirchhoff wave equations with nonlinear strongly damped terms: . Firstly, in order to prove the smoothing effect of the solution, we make efficient use of the analytic property of the semigroup generated by the principal operator of the equation in the phase space. Then we obtain the regularity of the global attractor and construct the approximate inertial manifold of the equation. Finally, we prove that arbitrary trajectory of the Kirchhoff wave equations goes into a small neighbourhood of the approximate inertial manifold after large time.