Global Attractor and Exponential Attractor for Higher-Order Kirchhoff Equations with Fading Memory
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LV Peng-hui, LIN Guo-guang, LV Xiao-jun
In this paper, we study the initial and boundary value problems of higher order Kirchhoff equation with higer-order memory term. Firstly, under approprate assumptions, we use Galerkin finite element method and a priori estimation to prove the existence and uniqueness of the global solution of this kind of equation in detail; and use contraction function menthod to prove the asymptotics of the solution semigroup, and then we get the existence of the global attractor ; in the end, we discuss the exponential attractor of a class of equations, and the finite fractal dimension of the global attractor is obtained.
Higher-order kirchhoff equation, Fading memory, Global attractor, Exponential attractor