Banach空间上有限时滞退化微分方程的适定性

Acta mathematica scientia,Series A ›› 2018, Vol. 38 ›› Issue (2): 264-275.

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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)

Abstract

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

CLC Number:

O177

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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References

[1] Lizama C, Ponce R. Periodic solutions of degenerate differential equations in vector-valued function spaces. Studia Math, 2011, 202(1):49-63
[2] 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
[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. L^p-maximal regularity of degenerate delay equations with periodic conditions. Banach J Math Anal, 2014, 8(2):49-59
[5] Cai G, Bu S. Periodic solutions of third-order degenerate differential equations in vector-valued functional spaces. Israel J Math, 2016, 212:163-188
[6] Arendt W, Bu S. The operator-valued Marcinkiewicz multiplier theorem and maximal regularity. Math Z, 2002, 240:311-343
[7] Arendt W, Bu S. Operator-valued Fourier multipliers on periodic Besov spaces and applications. Proc Edinb Math Soc, 2004, 47:15-33
[8] Bu S, Kim J. Operator-valued Fourier multipliers on periodic Triebel spaces. Acta Math Sin (Engl Ser), 2005, 21(5):1049-1056
[9] Favini A, Yagi A. Degenerate Differential Equations in Banach Spaces. New York:CRC Press, 1998
[10] Sviridyuk G, Fedorov V. Linear Type Equations and Degenerate Semigroups of Operators (Inverseans Ill-posed Probelms). Utrecht:De Gruyter, 2003
[11] Keyantuo V, Lizama C. Periodic solutions of second order differential equations in Banach spaces. Math Z, 2006, 253:489-514
[12] 蔡钢. Banach 空间中二阶退化微分方程的周期解.中国科学:数学, 2015, 45:381-392 Cai G. Periodic solution of second order degenerate differential equation in Banach spaces (in Chinese). Sci Sin Math, 2015, 45:381-392
[13] Chao J A, Woyczynski W A. Probability Theory and Harmonic Analysis. New York:Marcel Dekker Inc, 1986

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

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