Research ArticleOpen AccessGoogle Scholar indexed
Global Attractor for a Class of Nonlinear Generalized Kirchhoff-Boussinesq Model
Mathematical of Yunnan University, Kunming, China
Mathematical of Yunnan University, Kunming, China
Mathematical of Yunnan University, Kunming, China
- 1 Mathematical of Yunnan University, Kunming, China
- 2 Mathematical of Yunnan University, Kunming, China
- 3 Mathematical of Yunnan University, Kunming, China
International Journal of Modern Nonlinear Theory and Application·Volume 05 (2016)·Pages 82–92·Published 2 March 2016·DOI10.4236/ijmnta.2016.51009
Copy link · social · email
Abstract
In this paper, we study the long time behavior of solution to the initial boundary value problem for a class of Kirchhoff-Boussinesq model flow . We first prove the wellness of the solutions. Then we establish the existence of global attractor.
KeywordsKirchhoff-Boussinesq ModelStrongly DampedExistenceGlobal Attractor
- Chueshov, I. and Lasiecka, I. (2006) Existence, Uniqueness of Weak Solutions and Global Attractors for a Class of Nonlinear 2D Kirchhoff-Boussinesq Models. AIM Journals, 15, 777-809.
- Yang, Z. and Jin, B. (2009) Global Attractor for a Class of Kirchhoff Models. Journal of Mathematical Physics, 50, Article ID: 032701.
- Yang, Z., Feng, N. and Ma, T.F. (2015) Global Attractor for the Generalized Double Dispersion Equation. Nonlinear Analysis, 115, 103-116. http://dx.doi.org/10.1016/j.na.2014.12.006
- Ma, T.F. and Pelicer, M.L. (2013) Attractors for Weakly Damped Beam Equations with p-Laplacian. Discrete and Continuous Dynamical Systems. Supplement, 525-534.
- Yang, Z. and Liu, Z. (2015) Exponential Attractor for the Kirchhoff Equations with Strong Nonlinear Damping and Supercritial Nonlinearity. Applied Mathematics Letters, 46, 127-132. http://dx.doi.org/10.1016/j.aml.2015.02.019
- Kloeden, P.E. and Simsen, J. (2015) Attractors of Asymptotically Autonomous Quasi-Linear Parabolic Equation with Spatially Variable Exponents. Journal of Mathematical Analysis and Applications, 425, 911-918. http://dx.doi.org/10.1016/j.jmaa.2014.12.069
- Silva, M.A.J. and Ma, T.F. (2013) Long-Time Dynamics for a Class of Kirchhoff Models with Memory. Journal of Mathematical Physics, 54, Article ID: 021505.
- Lin, G.G., Xia, F.F. and Xu, G.G. (2013) The Global and Pullback Attractors for a Strongly Damped Wave Equation with Delays. International Journal of Modern Nonlinear Theory and Application, 2, 209-218. http://dx.doi.org/10.4236/ijmnta.2013.24029
- Guo, L., Yuan, Z.Q. and Lin, G.G. (2014) The Global Attractors for a Nonlinear Viscoelastic Wave Equation with Strong Damping and Linear Damping and Source Terms. International Journal of Modern Nonlinear Theory and Application, 4, 142-152. http://dx.doi.org/10.4236/ijmnta.2015.42010
- Lin, G.G. (2011) Nonlinear Evolution Equation. Yunnan University Press.