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.
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.