摘要
研究含有单参数的抽象Cauchy问题(OACP): u′(t)=A(t)u(t) t≥0, u(0)=x,其中{A(t)|t≥0)是一族线性算子。为了用半群的思想方法直接研究问题(OACP),引入了一类更广义的半群——C(t,s)半群,并由此发展和推广了有关半群的某些结果;同时,还讨论了C(t,s)半群与问题(OACP)之间的关系,从而可以把(OACP)问题的研究转化为C(t,s)半群的研究,开拓了探讨(OACP)问题的途径。
One-parameter abstract Cauchy problem (problem OACP, in short) is studied: u'(t)= A(t)u(t), t≥0, u(0)=x, where {A(t)|t≥0}is a family of linear operators on a Banach space. In order to study the problem (OACP) directly by means of semigroups, the concep of one new type semigroup. C(t,s) -semigroup is introduced, which has improved some theories established. The relation between C(t,s)-semigroup and problem (OACP) is also discussed.
出处
《西北大学学报（自然科学版）》
CAS
CSCD
1993年第5期409-413,共5页
Journal of Northwest University（Natural Science Edition）
关键词
半群
巴拿赫空间
抽象初值问题
the abstract Cauchy problem C(t,s)-semigroup strictly non-degeneracy of semigroup properly posed (OACP) problem
