非线性双曲方程的整体解的存在性|Blow up及生命跨度

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Abstract:

This paper proves the existence of global solutions and blow up for the Cauchy problem of some nonlinear hyperbolic equations with the initial energy of “critical value”,using the extreme principles of nonlinear functional, and gives the super estimate of nonlinear global solutions of life span for initial energy less than critical value.

Key words: Ｅｘｔｒｅｍｅｐｒｉｎｃｉｐｌｅｓ, Ｇｌｏｂａｌｓｏｌｕｔｉｏｎｓ, Ｔｈｅｐｒｏｂｌｅｍｏｆｂｌｏｗｕｐ, Ｌｉｆｅｓｐａｎ

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３５Ｌ

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Zhang Quande. On Global Existence,Blow Up and Life Span of Nonlinear Hyperbolic Equations[J].Acta mathematica scientia,Series A, 1999, 19(1): 45-52.

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References

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5 王明新，丁夏畦. 半线性热方程的整体解，渐近性与Blow up问题. 中国科学A辑，1992，10：1026-1034

6 L E Pane, P H Sattinger. Sadde points and instability of nonlinear hyperbolic equations. Isreal J of Math,1975,22:273-303

7 H A Levine. The role of critical exponents in blow up theorems. Siam Review,1990,32(2):262-288

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On Global Existence,Blow Up and Life Span of Nonlinear Hyperbolic Equations

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