| THE UNIQUENESS AND CONTINUOUS DEPENDENCE FOR CHARACTERISTIC CAUCHY PROBLEM OF PARTIAL DIFFERENTIAL EQUATIONS |
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| 引用本文： | 栾文贵,刘伟霞.THE UNIQUENESS AND CONTINUOUS DEPENDENCE FOR CHARACTERISTIC CAUCHY PROBLEM OF PARTIAL DIFFERENTIAL EQUATIONS[J].数学物理学报(B辑英文版),1995(4). |
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| 作者姓名： | 栾文贵 刘伟霞 |
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| 作者单位： | Luan Wengui(Computing Center，Academia Silica，Beijing，China.)Liu Weixia (Beijing Information Technology Institute，Beijing 100101，China.) |
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| 摘 要： | ＴＨＥＵＮＩＱＵＥＮＥＳＳＡＮＤＣＯＮＴＩＮＵＯＵＳＤＥＰＥＮＤＥＮＣＥＦＯＲＣＨＡＲＡＣＴＥＲＩＳＴＩＣＣＡＵＣＨＹＰＲＯＢＬＥＭＯＦＰＡＲＴＩＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＬｕａｎＷｅｎｇｕｉ（栾文贵）（ＣｏｍｐｕｔｉｎｇＣｅｎｔ...
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THE UNIQUENESS AND CONTINUOUS DEPENDENCE FOR CHARACTERISTIC CAUCHY PROBLEM OF PARTIAL DIFFERENTIAL EQUATIONS |
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| Luan Wengui.THE UNIQUENESS AND CONTINUOUS DEPENDENCE FOR CHARACTERISTIC CAUCHY PROBLEM OF PARTIAL DIFFERENTIAL EQUATIONS[J].Acta Mathematica Scientia,1995(4). |
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| Authors: | Luan Wengui |
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| Abstract: | in this paper, we investigate the connection between the uniqueness and the continuous dependence for the Cauchy problem of linear partial differential equations with everywhere characteristic initial hypersurface. The local Carleman's estimate used by S. Alinhac and M. S. Baouendi to prove the uniqueness for the characteristic Cauchy problem is improved to the global estimate with a specific peaking weight factor. Using this estimate, we can prove similarly the uniqueness of the characteristic Cauchy problem. In particular, we derive also the continuous dependence for the solution of this problem in the function class that a certain norm is bounded by the aid of the same inference of proving the global estimate. |
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| Keywords: | Pseudo-differential operators Factorization Estimation |
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