Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 164303, 9 pages
doi:10.1155/2009/164303
Research Article
Sharp Condition for Global Existence and Blow-Up on Klein-Gordon Equation
1School of Mathematical Sciences, Heilongjiang University, Harbin 150008, China
2Department of Mathematics, Mudanjiang Teachers College, Mudanjiang 157012, China
Received 26 November 2008; Revised 17 March 2009; Accepted 17 April 2009
Academic Editor: Ben T. Nohara
Copyright © 2009 Zhao Junsheng and Li Shufeng. 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.
Linked References
- H. Pecher, “-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen. I,” Mathematische Zeitschrift, vol. 150, no. 2, pp. 159–183, 1976. View at Zentralblatt MATH · View at MathSciNet
- 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. View at Zentralblatt MATH · View at MathSciNet
- L. E. Payne and D. H. Sattinger, “Saddle points and instability of nonlinear hyperbolic equations,” Israel Journal of Mathematics, vol. 22, no. 3-4, pp. 273–303, 1975. View at Zentralblatt MATH · View at MathSciNet
- J. M. Ball, “Finite time blow-up in nonlinear problems,” in Nonlinear Evolution Equations (Proc. Sympos., Univ. Wisconsin, Madison, Wis., 1977), M. G. Grandall, Ed., vol. 40 of Publications of the Mathematics Research Center, University of Wisconsin, pp. 189–205, Academic Press, New York, NY, USA, 1978. View at Zentralblatt MATH · View at MathSciNet
- W. A. Strauss, Nonlinear Wave Equations, CBMS Regional Conference Series in Mathematics, no. 73, American Mathematical Society, Providence, RI, USA, 1989. View at Zentralblatt MATH · View at MathSciNet
- J. Zhang, “Sharp conditions of global existence for nonlinear Schrödinger and Klein-Gordon equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 48, no. 2, pp. 191–207, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- L. Yacheng and Z. Junsheng, “On potential wells and applications to semilinear hyperbolic equations and parabolic equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 64, no. 12, pp. 2665–2687, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet