Sharp Condition for Global Existence and Blow-Up on Klein-Gordon Equation

Zhao Junsheng, Li Shufeng
2009 Mathematical Problems in Engineering  
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.
doi:10.1155/2009/164303 fatcat:4o4sgbyfqje4bfmlun2kvehk6e