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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.

Suggested Citation

  • Zhao Junsheng & Li Shufeng, 2009. "Sharp Condition for Global Existence and Blow-Up on Klein-Gordon Equation," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-9, July.
    • Handle: RePEc:hin:jnlmpe:164303
    DOI: 10.1155/2009/164303
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