| Triebel-Lizorkin空间上二阶有限时滞退化微分方程的适定性 |
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| 引用本文： | 蔡钢. Triebel-Lizorkin空间上二阶有限时滞退化微分方程的适定性[J]. 数学学报, 2018, 61(5): 741-750 |
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| 作者姓名： | 蔡钢 |
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| 作者单位： | 重庆师范大学数学科学学院 重庆 401331 |
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| 基金项目： | 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）及市高等学校青年骨干教师资助计划（020603011714）；重庆师范大学青年拔尖人才计划（02030307-00024） |
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| 摘 要： | 本文在周期Triebel-Lizorkin空间F_(p,q)~s(T;X)上研究二阶有限时滞退化微分方程(Mu')'(t)+αu'(t)=Au(t)Gu'_t+Fu_t+f(t)(t∈T:=[0,2π]),u(0)=u(2π),(Mu')(0)=(Mu')(2π)的适定性.利用Triebel-Lizorkin空间上算子值傅里叶乘子定理,给出上述方程是F_(p,q~-)~s适定的充要条件.
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Well-posedness of Second Order Degenerate Differential Equations with Finite Delay in Triebel-Lizorkin Spaces |
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| Gang CAI. Well-posedness of Second Order Degenerate Differential Equations with Finite Delay in Triebel-Lizorkin Spaces[J]. Acta Mathematica Sinica, 2018, 61(5): 741-750 |
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| Authors: | Gang CAI |
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| Affiliation: | School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P. R. China |
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| Abstract: | We study the second order degenerate differential equations with finite delay:(Mu')'(t) + αu'(t)=Au(t) + Gu't + Fut + f(t) (t ∈[0,2π]) with periodic boundary conditions u(0)=u(2π), (Mu)'(0)=(Mu)'(2π) in periodic Triebel-Lizorkin spaces. Using operator-valued Fourier multipliers theorems in Triebel-Lizorkin spaces Fp,qs(T; X), we give necessary and sufficient conditions for the Fp,qs-well-posedness of above equations. |
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| Keywords: | Triebel-Lizorkin spaces degenerate differential equations well-posedness Fourier multipliers |
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