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.