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For the model (1.1), it is originally in suspension bridge equations which were posed as a new problem in the field of nonlinear analysis [1] by Lazer and McKenna in 1990. In the suspension bridge system, suspension bridge can be regarded as an elastic beam with hinged ends ( or both fixed points). Lately, similar models have been studied by many authors, see [2-10]. Zhong et al.[2] investigated the existence of the strong solutions and strong global attractors for the single suspension bridge equations utilizing the condition (C) introduced [10] and the technique of energy estimates. In [3], the authors obtained exponential attractors of suspension bridge equation. Kang [4] considered the asymptotic behavior of the thermoelastic suspension bridge equation with past history. Besides, the problem of longtime behavior of the solutions to the suspension bridge equations has been studied by plently of authors [5-7]. In this article, under a weaker condition of the nonlinearity, we take advantage of the enhanced flattening property proposed by Li and Wu [8] to show the existence of exponential attractor for Kirchhoff type suspension equations with linear memory and polynomial damping.

The Exponential Attractor for Kirchhoff type Suspension Bridge Equations with Linear Memory and Polynomial Damping