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.
基金项目:
作者单位
张兴永 中国矿业大学数力系 
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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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