Research ArticleOpen AccessGoogle Scholar indexed
The Estimates of the Upper Bounds of Hausdorff Dimensions for the Global Attractor for a Class of Nonlinear Coupled Kirchhoff-Type Equations
Department of Mathematics, Yunnan University, Kunming, China
Department of Mathematics, Yunnan University, Kunming, China
- 1 Department of Mathematics, Yunnan University, Kunming, China
- 2 Department of Mathematics, Yunnan University, Kunming, China
Advances in Pure Mathematics·Volume 08 (2018)·Pages 1–10·Published 9 January 2018·DOI10.4236/apm.2018.81001
Copy link · social · email
Abstract
This paper deals with the Hausdorff dimensions of the global attractor for a class of Kirchhoff-type coupled equations with strong damping and source terms. We obtain a precise estimate of upper bound of Hausdorff dimension of the global attractor.
KeywordsKirchhoff-Type EquationsThe Global AttractorHausdorff Dimension
- Lin, G.G. and Zhang, M. (2017) The Global Attractors for a Class of Nonlinear Coupled Kirchhoff-Type Equations. European Journal of Mathematics and Computer Science, 4.
- Wu, J.Z. and Lin, G.G. (2009) The Global Attractor and Its Dimensions Estimation of Bossinesq Equation with Damping Term. Journal of Yunnan University, 31, 335-340.
- Fan, X.M. and Zhou, S.F. (2004) Kernel Sections for Non-Autonomous Strongly Damped Wave Equations of Non-Degenerate Krichhoff-Type. Applied Mathematics and Computation, 158, 253-266. https://doi.org/10.1016/j.amc.2003.08.147
- Lin, G.G. and Gao, Y.L. (2017) The Global and Exponential Attractors for the Higher-Order Kirchhoff-Type Equation with Strong Linear Damping. Journal of Mathematics Research, 9.
- Teman, R. (1988) Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Applied Mathematical Sciences, 68, Springer-Verlag, New York. https://doi.org/10.1007/978-1-4684-0313-8