Sharp Condition for Global Existence and Blow-Up on Klein-Gordon Equation release_4o4sgbyfqje4bfmlun2kvehk6e

by Zhao Junsheng, Li Shufeng

Published in Mathematical Problems in Engineering by Hindawi Limited.

2009   Volume 2009, p1-9

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.
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