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Sharp Condition for Global Existence and Blow-Up on Klein-Gordon Equation
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Zhao Junsheng, Li Shufeng
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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