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The Local Existence for Semilinear Wave Equations

The Local Existence for Semilinear Wave Equations
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摘要 The Cauchy problem for the semilinear wave equation has been studied and results show that the problem is locally well-posed in Hs ( Rn ) for s > max [ 0, n/2 - 1]. We extend the results by Lindblad in R3 to R2 and R1. The methods used in this paper are different from those of Lindblad and also the methods are more simple. The Cauchy problem for the semilinear wave equation has been studied and results show that the problem is locally well-posed in Hs ( Rn ) for s > max [ 0, n/2 - 1]. We extend the results by Lindblad in R3 to R2 and R1. The methods used in this paper are different from those of Lindblad and also the methods are more simple.
作者 Yang Han(杨晗) Lai Shaoyong(赖绍永)
机构地区 Department of Applied Mathematics
出处 《Journal of Southwest Jiaotong University(English Edition)》 2002年第2期134-138,共5页 西南交通大学学报（英文版）
基金 Supported by the fund of SWJTU (No. 1999XJ06)
关键词 semilinear wave equations Cauchy problem semilinear wave equations, Cauchy problem
分类号 O1 [理学—基础数学]
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参考文献9

  • 1[1]Klainerman S., Machedon M., Space-time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math., Vol.XIVI, No.10, 1993, 1221-1268.
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  • 5[5]Bournaveas N., Local existence of energy class solutions for the Dirac-Klein-Gordon equations, Comm. in Partial Differential Equations, Vol.24, No.6, 1999, 1167-1193.
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Journal of Southwest Jiaotong University(English Edition)
2002年 第2期

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