期刊目錄列表 - 42期革新版(1997.10) - 【數理與科技類】42期
Directory
Ｃ－半群與半線性方程式
作者:張幼賢、趙國欽（國立臺灣師範大學數學系）
卷期：42期（革新版）
日期：1997年10月
頁碼：25-52
DOI：10.6301/JNTNU.1997.42.03
摘要：
本文是考慮抽象半線性微分方程式
其中A是一個在Banach空間X上之C-半群的生成元， 為一個函數。我們給予函數f某些適當的條件，使得以上之抽象半線性方程式 (0.1) 有唯一的古典解、強解或弱解。我們也找出弱解存在的最大時間範圍，並探討此解在趨近邊界時的行為；此外，我們也證明了解對初值條件的連續性。為了證明這結 果，我們先證明 (0.1) 所對應的非齊次方程式
在給予非齊次項函數C某些適當的條件，使得以上之抽象非齊次微分方程式 (0.2) 有唯一的古典解、強解或弱解。本文最大之特色是無需假設這個C-半群是指數有界（exponential bounded）。
關鍵詞：C-正則半群、指數有界C-正則半群、抽象非齊次微分方程式、抽象半線性微分方程式
《詳全文》
Journal directory listing - Volume 42 (1997/October) - Mathematics, Science & Technology【42】
Directory
Abstract Semilinear Differential Equations and C- regularized semigroups
Author: Yu-Hsien Chang (Department of Mathematics, National Taiwan Normal University), Guo-Chin Jau (Department of Mathematics, National Taiwan Normal University)
Vol.&No.：Vol. 42 (New Version)
Date：October 1997
Pages：25-52
DOI：10.6301/JNTNU.1997.42.03
Abstract：
The main concern of this paper is under some suitable conditions on the forcing term and the op-erator A to find the unique classical solution, strong solution or mild solution for the abstract semilinear initial value problem:
where A is an infinitesimal generator of a C-semigroup is a Banach space. We also discussed the maximum interval of the existence for the mild solutions and contin-uous dependence of initial data. The basic technique used in this paper is the fixed point theory for dif-ferential equations in Banach space. For this purpose, we prove first that the corresponding inhomoge-neous equation
has a unique classical solution, strong solution or mild solution. However, the most enjoy here is that we do not need to assume that the C-semigroup is exponentially bounded.
Keywords：C-regularized semigroups, exponentially bounded C-regularized semigroups, abstract in-homogeneous differential equations, abstract semilinear differential equations