Triebel—Lizorkin空间上二阶有限时滞退化微分方程的适定性

蔡钢

数学学报 ›› 2018, Vol. 61 ›› Issue (5) : 741-750.

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数学学报 ›› 2018, Vol. 61 ›› Issue (5) : 741-750. DOI: 10.12386/A2018sxxb0068
论文

Triebel—Lizorkin空间上二阶有限时滞退化微分方程的适定性

    蔡钢
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Well-posedness of Second Order Degenerate Differential Equations with Finite Delay in Triebel-Lizorkin Spaces

    Gang CAI
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摘要

本文在周期Triebel—Lizorkin空间Fp,qs(T;X)上研究二阶有限时滞退化微分方程(Mu')'(t)+αu'(t)=Aut)+Gu't+Fut+ft)(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Fp,qs-适定的充要条件.

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.

关键词

Triebel-Lizorkin空间 / 退化微分方程 / 适定性 / 傅里叶乘子

Key words

Triebel-Lizorkin spaces / degenerate differential equations / well-posedness / Fourier multipliers

引用本文

导出引用
蔡钢. Triebel—Lizorkin空间上二阶有限时滞退化微分方程的适定性. 数学学报, 2018, 61(5): 741-750 https://doi.org/10.12386/A2018sxxb0068
Gang CAI. Well-posedness of Second Order Degenerate Differential Equations with Finite Delay in Triebel-Lizorkin Spaces. Acta Mathematica Sinica, Chinese Series, 2018, 61(5): 741-750 https://doi.org/10.12386/A2018sxxb0068

参考文献

[1] Arendt W., Bu S., The operator-valued Marcinkiewicz multiplier theorem and maximal regularity, Math. Z., 2002, 240:311-343.
[2] Arendt W., Bu S., Operator-valued Fourier multipliers on periodic Besov spaces and applications, Proc. Edinb. Math. Soc., 2004, 47:15-33.
[3] Bu S., Well-posedness of second order degenerate differential equations in vector-valued function spaces, Studia Math., 2013, 214(1):1-16.
[4] Bu S., Lp-maximal regularity of degenerate delay equations with periodic conditions, Banach J. Math. Anal., 2014, 8(2):49-59.
[5] Bu S., Cai G., Periodic solutions of third-order degenerate differential equations in vector-valued functional spaces, Pacific J. Math., 2017, 288(1):27-46.
[6] Bu S., Kim J., Operator-valued Fourier multipliers on periodic Triebel spaces, Acta Math. Sin. Engl. Ser., 2005, 21(5):1049-1056.
[7] Cai G., Bu S., Periodic solutions of third-order degenerate differential equations in vector-valued functional spaces, Israel J. Math., 2016, 212:163-188.
[8] Favini A., Yagi A., Degenerate differential equations in Banach spaces, Pure Appl. Math., 1999, 215, Dekker, New York.
[9] Lizama C., Ponce R., Periodic solutions of degenerate differential equations in vector-valued function spaces, Studia Math., 2011, 202(1):49-63.
[10] Lizama C., Ponce R., Maximal regularity for degenerate differential equations with infinite delay in periodic vector-valued function spaces, Proc. Edinb. Math. Soc., 2013, 56:853-871.
[11] Sviridyuk G., Fedorov V., Linear sobolev type equations and degenerate semigroups of operators, Inverse Ill-posed Probel. Ser., 2003, VSP, Utrecht.

基金

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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