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

Zhao Junsheng1 and Li Shufeng2

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.

Abstract

We study the initial boundary value problem of the nonlinear Klein-Gordon equation. First we introduce a family of potential wells. By using them, we obtain a new existence theorem of global solutions and show the blow-up in finite time of solutions. Especially the relation between the above two phenomena is derived as a sharp condition.