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Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (2): 150-154.

• 论文 • 上一篇    下一篇

GLOBAL SOLUTION OF THE INVERSE PROBLEM FOR A CLASS OF NONLINEAR EVOLUTION EQUATIONS OF DISPERSIVE TYPE

陈芳启1,3, 陈予恕2, 吴志强2   

  1. 1. Department of Mathematics, Tianjin University, Tianjin 300072, P R China;
    2. Department of Mechanics, Tianjin University, Tianjin 300072, P R China;
    3. Liuhui Center for Applied Mathematics, Nankai University, Tianjin 300072, P R China
  • 收稿日期:2000-10-24 修回日期:2001-10-09 出版日期:2002-02-18 发布日期:2002-02-18
  • 基金资助:

    the National Natural Science Foundation of China(Significance 19990510);the National Key Basic Research Special Foundation of China(G1998020316);Liuhui Center for Applied Mathematics,Nankai University & Tianjin University

GLOBAL SOLUTION OF THE INVERSE PROBLEM FOR A CLASS OF NONLINEAR EVOLUTION EQUATIONS OF DISPERSIVE TYPE

CHEN Fang-qi1,3, CHEN Yu-shu2, WU Zhi-qiang2   

  1. 1. Department of Mathematics, Tianjin University, Tianjin 300072, P R China;
    2. Department of Mechanics, Tianjin University, Tianjin 300072, P R China;
    3. Liuhui Center for Applied Mathematics, Nankai University, Tianjin 300072, P R China
  • Received:2000-10-24 Revised:2001-10-09 Online:2002-02-18 Published:2002-02-18
  • Supported by:

    the National Natural Science Foundation of China(Significance 19990510);the National Key Basic Research Special Foundation of China(G1998020316);Liuhui Center for Applied Mathematics,Nankai University & Tianjin University

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摘要： The inverse problem for a class of nonlinear evolution equations of dispersive type was reduced to Cauchy problem of nonlinear evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to the inverse problem discussed here. The existence and uniqueness theorem of global solution was given for this class of nonlinear evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence and uniqueness of local solution presented by YUAN Zhong-xin.

Abstract: The inverse problem for a class of nonlinear evolution equations of dispersive type was reduced to Cauchy problem of nonlinear evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to the inverse problem discussed here. The existence and uniqueness theorem of global solution was given for this class of nonlinear evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence and uniqueness of local solution presented by YUAN Zhong-xin.

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