- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
International Journal of Differential Equations
Volume 2014 (2014), Article ID 724837, 5 pages
Global and Blow-Up Solutions for Nonlinear Hyperbolic Equations with Initial-Boundary Conditions
1Department of Mathematics, Faculty of Science, Gazi University, Teknikokullar, Ankara, Turkey
2Incirli Mahallesi, Karaelmas Sokak, Yunusemre Caddesi 51/18, İncirli, Ankara, Turkey
Received 24 December 2013; Revised 7 March 2014; Accepted 20 March 2014; Published 13 April 2014
Academic Editor: D. D. Ganji
Copyright © 2014 Ülkü Dinlemez and Esra Aktaş. 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.-Q. Wu and S.-J. Li, “Global solution and blow-up solution for a nonlinear damped beam with source term,” Applied Mathematics, vol. 25, no. 4, pp. 447–453, 2010.
- H. A. Levine, P. Pucci, and J. Serrin, “Some remarks on global nonexistence for nonautonomous abstract evolution equations,” Contemporary Mathematics, vol. 208, pp. 253–263, 1997.
- H. A. Levine and J. Serrin, “Global nonexistence theorems for quasilinear evolution equations with dissipation,” Archive for Rational Mechanics and Analysis, vol. 137, no. 4, pp. 341–361, 1997.
- V. Georgiev and G. Todorova, “Existence of a solution of the wave equation with nonlinear damping and source terms,” Journal of Differential Equations, vol. 109, no. 2, pp. 295–308, 1994.
- J. Hao and S. Li, “Global solutions and blow-up solutions for a nonlinear string with boundary input and output,” Nonlinear Analysis: Theory, Methods and Applications, vol. 66, no. 1, pp. 131–137, 2007.
- Ü. Dinlemez, “Global existence, uniqueness of weak solutions and determining functionals for nonlinear wave equations,” Advances in Pure Mathematics, vol. 3, pp. 451–457, 2013.
- Y. Guo and M. A. Rammaha, “Global existence and decay of energy to systems of wave equations with damping and supercritical sources,” Zeitschrift für Angewandte Mathematik und Physik, vol. 64, no. 3, pp. 621–658, 2013.
- L. Bociu, M. Rammaha, and D. Toundykov, “On a wave equation with supercritical interior and boundary sources and damping terms,” Mathematische Nachrichten, vol. 284, no. 16, pp. 2032–2064, 2011.
- C. O. Alves, M. M. Cavalcanti, V. N. Domingos Cavalcanti, M. A. Rammaha, and D. Toundykov, “On existence, uniform decay rates and blow up for solutions of systems of nonlinear wave equations with damping and source terms,” Discrete and Continuous Dynamical Systems, vol. 2, no. 3, pp. 583–608, 2009.
- M. M. Cavalcanti, V. N. Domingos Cavalcanti, and I. Lasiecka, “Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction,” Journal of Differential Equations, vol. 236, no. 2, pp. 407–459, 2007.
- C. O. Alves and M. M. Cavalcanti, “On existence, uniform decay rates and blow up for solutions of the 2-D wave equation with exponential source,” Calculus of Variations and Partial Differential Equations, vol. 34, no. 3, pp. 377–411, 2009.
- M. A. Rammaha, “The influence of damping and source terms on solutions of nonlinear wave equations,” Boletim da Sociedade Paranaense de Matemática, vol. 25, no. 1-2, pp. 77–90, 2007.
- V. Barbu, I. Lasiecka, and M. A. Rammaha, “Existence and uniqueness of solutions to wave equations with nonlinear degenerate damping and source terms,” Control and Cybernetics, vol. 34, no. 3, pp. 665–687, 2005.
- M. M. Cavalcanti and V. N. Domingos Cavalcanti, “Existence and asymptotic stability for evolution problems on manifolds with damping and source terms,” Journal of Mathematical Analysis and Applications, vol. 291, no. 1, pp. 109–127, 2004.
- M. M. Cavalcanti, V. N. D. Cavalcanti, J. S. Prates Filho, and J. A. Soriano, “Existence and uniform decay of solutions of a parabolic-hyperbolic equation with nonlinear boundary damping and boundary source term,” Communications in Analysis and Geometry, vol. 10, no. 3, pp. 451–466, 2002.