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Author: 王啟光
Chii Guang Wang
Thesis Title: 高階非線性方程問題之探討
Higher order abstract Cauchy problem
Advisor: 張幼賢
Chang, Yu-Hsien
Degree: 碩士
Master
Department: 數學系
Department of Mathematics
Thesis Publication Year: 2000
Academic Year: 88
Language: 中文
Number of pages: 19
Keywords (in Chinese): 高階抽象柯西問題
Keywords (in English): Higher order abstract Cauchy problem with initial data
Thesis Type: Academic thesis/ dissertation
Reference times: Clicks: 177Downloads: 7
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摘要
本篇論文主要是探討下列在 Banach 空間X上的高階抽象柯西問題(Higher order abstract Cauchy problem with initial data),
其中Ai 為在X上 C0半群的生成元,滿足某些條件,且f(t,u) 亦滿足某些適當條件下,我們證明了解的存在性和唯一性,並得到解的表現式。

This paper discusses the higher order abstract Cauchy problem with initial data on a Banach space X.Where Ai is a C0-semigroup
on X.We get the existance,uniqueness,and presentation of solution.

1.摘要 2.簡介 4.主要結果 16.應用 19.參考文獻

[1] G.R. Goldstein, J.A. Goldstein,and E.Obrecht, Structure of solution to linear evolution
equations:extensions of d'Alembert formula, J. Math.Anal.Appl.,201(1996),no.2,
461-477.
[2] J.A. Goldstein, J.T. Sandefur, An abstract d'Alembert formula, SIAM J. Math.Anal.
18(1987),no.3,842-856.
[3] J.A. Goldstein, R. Delaubenfels, and J.T Sandefur, Regularized semigroups,iterated
Cauchy problems and equipartition of energy, Mh. Math.,115(1993),47-66.
[4] E. Hille,and R.H.Phillips, Functional Analysis and Semigroups, Amer.Math. Soc.,
Providence, 1957.
[5] J.T. Sandefur,Jr., Higher order abstract Cauchy problems, J. Math. Anal. Appl., 60
(1977), 728-742.
[6] S.Yakubov, Y.Yakubov, Generalization of the d'Alembert formula and the Fourier
Method,Semigroup Forum 58 (1999),no.1 , 85-93.
[7] A.Pazy, Semigroups of Linear Operators and Applications to Partial Differential
Equations, Springer-Verlag New York, Inc.(1983).
[8] Ivar Stakgold, Green's Functions and Boundary Value Problems, A Wiley-Interscience
publication.(1998)second edition.

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