- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- 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
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 535031, 10 pages
On Global Solutions for the Cauchy Problem of a Boussinesq-Type Equation
Department of Mathematics, Dicle University, 21280 Diyarbakir, Turkey
Received 4 May 2012; Accepted 11 June 2012
Academic Editor: Valery Covachev
Copyright © 2012 Hatice Taskesen et al. 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.
- N. Polat and A. Ertaş, “Existence and blow-up of solution of Cauchy problem for the generalized damped multidimensional Boussinesq equation,” Journal of Mathematical Analysis and Applications, vol. 349, no. 1, pp. 10–20, 2009.
- R. Xue, “Local and global existence of solutions for the Cauchy problem of a generalized Boussinesq equation,” Journal of Mathematical Analysis and Applications, vol. 316, no. 1, pp. 307–327, 2006.
- N. Polat, “Existence and blow up of solutions of the Cauchy problem of the generalized damped multidimensional improved modified Boussinesq equation,” Zeitschrift Für Naturforschung A, vol. 63, pp. 1–10, 2008.
- Q. Lin, Y. H. Wu, and S. Lai, “On global solution of an initial boundary value problem for a class of damped nonlinear equations,” Nonlinear Analysis, vol. 69, no. 12, pp. 4340–4351, 2008.
- N. Polat and D. Kaya, “Blow up of solutions for the generalized Boussinesq equation with damping term,” Zeitschrift Für Naturforschung A, vol. 61, pp. 235–238, 2006.
- Y. Liu and R. Xu, “Global existence and blow up of solutions for Cauchy problem of generalized Boussinesq equation,” Physica D, vol. 237, no. 6, pp. 721–731, 2008.
- Q. Lin, Y. H. Wu, and R. Loxton, “On the Cauchy problem for a generalized Boussinesq equation,” Journal of Mathematical Analysis and Applications, vol. 353, no. 1, pp. 186–195, 2009.
- X. Runzhang, “Cauchy problem of generalized Boussinesq equation with combined power-type nonlinearities,” Mathematical Methods in the Applied Sciences, vol. 34, no. 18, pp. 2318–2328, 2011.
- J. A. Esquivel-Avila, “Dynamics around the ground state of a nonlinear evolution equation,” Nonlinear Analysis, vol. 63, no. 5–7, pp. 331–343, 2005.
- R. Xu, Y. Liu, and B. Liu, “The Cauchy problem for a class of the multidimensional Boussinesq-type equation,” Nonlinear Analysis, vol. 74, no. 6, pp. 2425–2437, 2011.
- Y.-Z. Wang and Y.-X. Wang, “Existence and nonexistence of global solutions for a class of nonlinear wave equations of higher order,” Nonlinear Analysis, vol. 72, no. 12, pp. 4500–4507, 2010.
- S. Wang and G. Xu, “The Cauchy problem for the Rosenau equation,” Nonlinear Analysis, vol. 71, no. 1-2, pp. 456–466, 2009.
- N. Kutev, N. Kolkovska, M. Dimova, and C. I. Christov, “Theoretical and numerical aspects for global existence and blow up for the solutions to Boussinesq paradigm equation,” AIP Conference Proceedings, vol. 1404, pp. 68–76, 2011.
- E. H. Lieb, “Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities,” Annals of Mathematics, vol. 118, no. 2, pp. 349–374, 1983.
- H. A. Levine, “Instability and nonexistence of global solutions to nonlinear wave equations of the form ,” Transactions of the American Mathematical Society, vol. 192, pp. 1–21, 1974.