| 张兴永.一类Laplace双曲型方程广义Cauchy问题的反问题[J].数学研究及应用,1995,15(2):271~274 |
| 一类Laplace双曲型方程广义Cauchy问题的反问题 |
| A Class of Inverse Problem for the General Gauchy Problem of the Laplace Hyperbolic Equation |
| 投稿时间：1992-03-22 修订日期：1994-04-19 |
| DOI：10.3770/j.issn:1000-341X.1995.02.022 |
| 中文关键词: 反问题 双曲型方程 积分方程组 Cauchy问题 局部解。 |
| 英文关键词:inverse problem hyperbolic type equation integral equation. |
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| 中文摘要: |
| 本文讨论了确定Ｌａｐｌｉｔｃｅ双曲型方程uxy(x,y)+a(x,y)ux(x,y)+b(x,y)+uy(x,y)+q(x)u(x,y)=f(x,y)的广义Ｃａｕｃｈｙ问题中系数ｑ（ｘ）的反问题。文中利用特征法线及不动点理论，导出了与反问题等价的非线性积分方程组，证明了反问题局部解的存在唯一性，最后给出了反问题整体用的唯一性定理。 |
| 英文摘要: |
| We determine the coefficient q(x)in the inverse problem of generaI Cauchy problem ofhyperbolic equation Uxy(x,y)+a(x,y)Ux(x,y)+b(x,y)+Uy(x,y)+q(x)U(x,y)=f(x,y).The nonline integral equations which is equivalent to the inverse problem have been ob-tained and the existence, uniqueness of local solution for the inverse problem has beenproved by the method of characteristic curves and the fixed point theorem. Finally,wegive a theorem on the uniqueness of whole solution for the inverse problem. |
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