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International Journal of Mathematical Analysis and Applications

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Exponential Attractor For a class of Higher-Order Coupled Kirchhoff-type Equations

International Journal of Mathematical Analysis and Applications
Vol.5 , No. 3, Publication Date: Jun. 1, 2018, Page: 49-57

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Authors

[1]	Guoguang Lin, Department of Mathematics, University of Yunnan, Kunming, China.
[2]	Sanmei Yang, Department of Mathematics, University of Yunnan, Kunming, China.

Abstract

This paper mainly studies a class of higher-order coupled Kirchhoff-type equations with strongly damping and nonlinear source terms. In the process of research, first of all, Lipschitz property of the nonlinear semi-group related to the initial boundary value problem is proved by applying the Young inequality, Poincare inequality, mean value theorem, Gronwall’s inequality and so on. Then, the Discrete Squeezing property of the problem is proved by applying the boundedness of this problem in infinite dimensional space and making some changes on the left hand side of the inequality to be proved. Finally, the existence of exponential attractor is proved by using the Lipschitz property, Discrete Squeezing property and other relevant proofs of the problem.

Keywords

Higher-order Coupled Kirchhoff-type Equations, Exponential Attractor, Lipschitz Property, Discrete Squeezing Property

Reference

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