EXISTENCE, UNIQUENESS, AND STABILITY OF NON-LINEAR EVOLUTION EQUATIONS

被引：9
作者：
ICHIKAWA, A
PRITCHARD, AJ
机构：
[1] Control Theory Centre, University of Warwick, Coventry
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 1979年 / 68卷 / 02期
关键词：
D O I：
10.1016/0022-247X(79)90129-X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study existence, uniqueness, and stability of nonlinear evolution equations. We develop a new type of perturbation result for a C0 semigroup in Banach space, where the nonlinear operators are not necessarily m-accretive or everywhere defined. Assuming that the semigroup has a smoothing property we obtain local existence, uniqueness and regularity results. We then establish a Liapunov theory which enables us to examine stability. To illustrate our theory several simple examples are presented. © 1979.
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页码：454 / 476
页数：23
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