一类非线性色散型发展方程反问题的整体解

基金项目: 国家自然科学基金资助项目(重大19990510);国家重点基础研究基金资助项目(G1998020316);南开大学天津大学刘徽应用数学中心资助项目

Global Solution of the Inverse Problem for a Class of Nonlinear Evolution Equations of Dispersive Type

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 University, TianJin 300072, P R China

摘要: 将一类非线性色散型发展方程反问题转化为抽象空间非线性发展方程Cauchy问题。利用半群方法和赋等价范数技巧,建立了该类抽象发展方程整体解的存在唯一性定理,并应用于所论反问题,得到了该类非线性色散型发展方程反问题整体解的存在唯一性定理,本质地改进了袁忠信得出的解的局部存在唯一性结果。
- 伪抛物方程 /
- 非线性发展方程 /
- 反问题
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 Zhongxin.
- pseudo-parabolic equation /
- nonlinear evolution equation /
- inverse problem

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