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Babin, A.V. and Vishik, M.I. (1992) Attractors of Evolution Equations. Attractors of Evolution Equations, North-Holland, Amsterdam.

has been cited by the following article:

• TITLE: The Exponential Attractor for a Class of Kirchhoff-Type Equations with Strongly Damped Terms and Source Terms

  AUTHORS: Guoguang Lin, Xiangshuang Xia

  KEYWORDS: Exponential Attractor, Inertial Fractal Set, Lipschitz Continuous, Squeezing Property

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.6 No.7, July 24, 2018

  ABSTRACT: This paper studies the exponential attractor for a class of the Kirchhoff-type equations with strongly damped terms and source terms. The exponential attractor is also called the inertial fractal set, which is an intermediate step between global attractors and inertial manifolds. Obtaining a set that attracts all the trajectories of the dynamical system at an exponential rate by the methods of Eden A. Under appropriate assumptions, we firstly construct an invariantly compact set. Secondly, showing the solution semigroups of the Kirchhoff-type equations is squeezing and Lipschitz continuous. Finally, the finite fractal dimension of the exponential attractor is obtained.