查詢結果分析
來源資料
頁籤選單縮合
題名 | Abstract Semilinear Differential Equations and C-regularized Semigroups=C-半群與半線性方程式 |
---|---|
作者 | 張幼賢; 趙國欽; | 書刊名 | 師大學報. 數理與科技類 |
卷期 | 42 1997.10[民86.10] |
頁次 | 頁25-52 |
分類號 | 314.5 |
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; C-regularized semigroups; Exponentially bounded C-regularized semigroups; Abstract inhomogeneous differential equations; Abstract semilinear differential equations; |
語文 | 英文(English) |
中文摘要 | 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)。 |
英文摘要 | 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. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。