簡易檢索 / 詳目顯示

研究生: 王啟光
Chii Guang Wang
論文名稱: 高階非線性方程問題之探討
Higher order abstract Cauchy problem
指導教授: 張幼賢
Chang, Yu-Hsien
學位類別: 碩士
Master
系所名稱: 數學系
Department of Mathematics
論文出版年: 2000
畢業學年度: 88
語文別: 中文
論文頁數: 19
中文關鍵詞: 高階抽象柯西問題
英文關鍵詞: Higher order abstract Cauchy problem with initial data
論文種類: 學術論文
相關次數: 點閱:178下載:7
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 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.

    QR CODE