The Exponential Attractor for a Class of Nonlinear Coupled Kirchhoff Equations with Strong Linear Damping

Abstract

This paper investigates the dynamics for a class of nonlinear higher-order coupled Kirchhoff equations with strong linear damping. By means of the method proposed by Eden et al., the Lipschitz continuity and the discrete squeezing property of its solution semigroup are proved, and thus the existence of the exponential attractor is obtained.Keywords: higher-order Kirchhoff-type, Lipschitz continuity, discrete squeezing property, exponential attractor Ma, Q. Z and her students considered the existence of exponential attractor with method proposed by Eden et al. Through

Global Nonexistence of the Higher Order Kirchhoff Type System With Logarithmic Nonlinearities

“…In the case M (s) = 1, m > 1 the single form of the problem (1.1) without logarithmic source terms have been discussed by many authors (see [12,16,15,11]).…”

Estimate on the Dimension of Global Attractor for Nonlinear Higher-Order Coupled Kirchhoff Type Equations

“…G. G. Lin and L. J., Hu have studied the existence of a global attractor for coupled Kirchhoff type equations with strongly linear damping in [1]. In this paper, we are concerned with the finite dimensions of the global attractor as where Ω is a bounded domain in n R with smooth boundary ∂Ω , , in .…”