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

CHEN Fang-qi; CHEN Yu-shu; WU Zhi-qiang

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Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(2): 139-143

CHEN Fang-qi, CHEN Yu-shu, WU Zhi-qiang. Global Solution of the Inverse Problem for a Class of Nonlinear Evolution Equations of Dispersive Type[J]. Applied Mathematics and Mechanics, 2002, 23(2): 139-143.

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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

Received Date: 2000-10-24
Rev Recd Date: 2001-10-09
Publish Date: 2002-02-15

Abstract

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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References(6)

References

[1]	袁忠信.一类非线性色散型发展方程的反问题[J].应用数学学报,1991,14(2):174-179.
[2]	Showalter R E,Ting T W.Pseudo parabolic partial differential equation[J].SIAM Math Anal,1970,1(1):1-26.
[3]	Pazy A.Semigroup of Linear Operators and Applications to Partial Differential Equation[M].New York:Springer-Verlag,1983,162-177.
[4]	Friedman A.Partial Differential Equations[M].New York:Holt,Rinehart and Winston,Inc,1969,83-92.
[5]	齐民友.线性偏微分算子引论[M].上册.北京:科学出版社,1986,410-411.
[6]	Deimling K.Nonlinear Functional Analysis[M].Berlin:Springer-Verlag,1985,137-144.