抽象空间中微分系统弱解的局部存在性

The Local Existence of Weak Solutions for Differential System in Abstract Spaces

考虑在抽象空间中，微分系统ｚ′＝ｘ′ｙ′＝ｆ１（ｔ，ｘ，ｙ）ｆ２（ｔ，ｘ，ｙ）＝ｆ（ｔ，ｚ）ｚ（０）＝ｘ（０）ｙ（０）＝ｚ０＝ｘ０ｙ０弱解的局部存在性，其中ｆ１、ｆ２分别满足弱紧性条件与弱耗散性条件．得到的结果包含了文［２～４，６］的有关结果，是上述结果的改进和更一般化推广．

Abstract In this paper, we are concerned the problem of the problem of the local existence of weak solutions for z ′=x ′ y ′=f 1(t,x,y) f 2(t,x,y)=f(t,z) z(0)=x(0) y(0)=z 0=x 0 y 0 in abstract space E, where f 1, f 2 meet weak noncompact condition and weak dissipative condition respectively. The results in this paper extened and improved the results in .