- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Advances in Mathematical Physics
Volume 2013 (2013), Article ID 364165, 7 pages
Global Existence and Asymptotic Behavior of Solutions to the Generalized Damped Boussinesq Equation
1School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, China
2College of Science, Henan Institute of Engineering, Zhengzhou 450001, China
Received 26 January 2013; Accepted 12 July 2013
Academic Editor: B. G. Konopelchenko
Copyright © 2013 Yinxia Wang and Hengjun Zhao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. Boussinesq, “Théorie des ondes et des remous qui se propagent le long dùn canal rectangu-laire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond,” Journal de Mathématiques Pures et Appliquées, vol. 17, pp. 55–108, 1872.
- V. Varlamov, “On the Cauchy problem for the damped Boussinesq equation,” Differential and Integral Equations, vol. 9, no. 3, pp. 619–634, 1996.
- V. Varlamov, “Existence and uniqueness of a solution to the Cauchy problem for the damped Boussinesq equation,” Mathematical Methods in the Applied Sciences, vol. 19, no. 8, pp. 639–649, 1996.
- V. V. Varlamov, “Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions,” International Journal of Mathematics and Mathematical Sciences, vol. 22, no. 1, pp. 131–145, 1999.
- W.-R. Dai and D.-X. Kong, “Global existence and asymptotic behavior of classical solutions of quasilinear hyperbolic systems with linearly degenerate characteristic fields,” Journal of Differential Equations, vol. 235, no. 1, pp. 127–165, 2007.
- D.-X. Kong and T. Yang, “Asymptotic behavior of global classical solutions of quasilinear hyperbolic systems,” Communications in Partial Differential Equations, vol. 28, no. 5-6, pp. 1203–1220, 2003.
- M. Nakao and K. Ono, “Existence of global solutions to the Cauchy problem for the semilinear dissipative wave equations,” Mathematische Zeitschrift, vol. 214, no. 2, pp. 325–342, 1993.
- K. Nishihara, “- estimates of solutions to the damped wave equation in 3-dimensional space and their application,” Mathematische Zeitschrift, vol. 244, no. 3, pp. 631–649, 2003.
- K. Ono, “Global existence and asymptotic behavior of small solutions for semilinear dissipative wave equations,” Discrete and Continuous Dynamical Systems A, vol. 9, no. 3, pp. 651–662, 2003.
- Z. Yang, “Longtime behavior of the Kirchhoff type equation with strong damping on ,” Journal of Differential Equations, vol. 242, no. 2, pp. 269–286, 2007.
- Y. Sugitani and S. Kawashima, “Decay estimates of solutions to a semilinear dissipative plate equation,” Journal of Hyperbolic Differential Equations, vol. 7, no. 3, pp. 471–501, 2010.
- Y.-X. Wang and Z. Wei, “Global existence and asymptotic behavior of solutions to Cahn-Hilliard equation with inertial term,” International Journal of Mathematics, vol. 23, no. 9, p. 1250087, 14, 2012.
- Y. Wang, “Existence and asymptotic behavior of solutions to the generalized damped Boussinesq equation,” Electronic Journal of Differential Equations, no. 96, 11 pages, 2012.
- Y.-Z. Wang, F. Liu, and Y. Zhang, “Global existence and asymptotic behavior of solutions for a semi-linear wave equation,” Journal of Mathematical Analysis and Applications, vol. 385, no. 2, pp. 836–853, 2012.
- Y.-Z. Wang and Y.-X. Wang, “Global existence and asymptotic behavior of solutions to a nonlinear wave equation of fourth-order,” Journal of Mathematical Physics, vol. 53, no. 1, p. 013512, 13, 2012.
- S. Kawashima and Y. Z. Wang, “Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation,” Analysis and Applications. In press.
- S. Wang and H. Xu, “On the asymptotic behavior of solution for the generalized IBq equation with hydrodynamical damped term,” Journal of Differential Equations, vol. 252, no. 7, pp. 4243–4258, 2012.
- T. T. Li and Y. M. Chen, Nonlinear Evolution Equations, Scientific Press, 1989, (Chinese).
- S. Zheng, Nonlinear Evolution Equations, vol. 133 of Monographs and Surveys in Pure and Applied Mathematics, Chapman & Hall, 2004.