Journal directory listing - Volume 42 (1997/October) - Mathematics, Science & Technology【42】

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


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

《Full Text》

APA FormatChang, Y.-H. & Jau, G.-C. (1997). Abstract semilinear differential equations and C- regularized semigroups. Journal of National Taiwan Normal University: Mathematics, Science & Technology, 42(New Version), 25-52.