Banach空间上有限时滞退化微分方程的适定性

数学物理学报 ›› 2018, Vol. 38 ›› Issue (2): 264-275.

Banach空间上有限时滞退化微分方程的适定性

蔡钢

重庆师范大学数学科学学院重庆 401331

收稿日期:2017-03-08 修回日期:2017-07-09 出版日期:2018-04-26 发布日期:2018-04-26
作者简介:蔡钢,E-mail:caigang-aaaa@163.com
基金资助:
国家自然科学基金（11401063，11771063）、重庆市自然科学基金（cstc2017jcyjAX0006）、重庆市教委项目（KJ1703041）、重庆市高等学校青年骨干教师资助计划（020603011714）和重庆师范大学青年拔尖人才计划（02030307-00024）

The Well-Posedness of Degenerate Differential Equations with Finite Delay in Banach Spaces

Cai Gang

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331

Received:2017-03-08 Revised:2017-07-09 Online:2018-04-26 Published:2018-04-26
Supported by:
Supported by the NSFC (11401063, 11771063), the Natural Science Foundation of Chongqing (cstc2017jcyjAX0006), the Science and Technology Project of Chongqing Education Committee (KJ1703041), the University Young Core Teacher Foundation of Chongqing (020603011714) and Talent Project of Chongqing Normal University (02030307-00024)

摘要/Abstract

摘要： 该文在Lebesgue-Bochner空间L^p（T，X）和周期Besov空间B_p，q^s（T，X）上研究二阶有限时滞退化微分方程：（Mu'）'（t）=Au（t）+Bu'（t）+Fu_t+f（t）（t ∈ T：=[0，2π]），u（0）=u（2π），（Mu'）（0）=（Mu'）（2π）的适定性.利用向量值函数空间上的算子值傅里叶乘子定理，文中给出上述方程具有适定性的充要条件.

关键词: Lebesgue-Bochner空间, Besov空间, 傅里叶乘子, 适定性

Abstract: In this paper, we study the well-posedness of the second order degenerate differential equation:(Mu')'(t)=Au(t) + Bu'(t) + Fu_t + f(t) (t ∈ T:=[0, 2π]) with periodic boundary conditions u(0)=u(2π),(Mu')(0)=(Mu')(2π), in Lebesgue-Bochner spaces L^p(T, X) and periodic Besov spaces B_p,q^s(T, X). Using operator-valued Fourier multipliers theorems in vector-valued function spaces, we give necessary and sufficient conditions for the well-posedness of above equation.

Key words: Lebesgue-Bochner spaces, Besov spaces, Fourier multipliers, Well-posedness

中图分类号:

O177

蔡钢. Banach空间上有限时滞退化微分方程的适定性[J]. 数学物理学报, 2018, 38(2): 264-275.

Cai Gang. The Well-Posedness of Degenerate Differential Equations with Finite Delay in Banach Spaces[J]. Acta mathematica scientia,Series A, 2018, 38(2): 264-275.

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