[1] Xue Xingmei, Lü Zhong,. Nonlocal controllability for semilinear problems in Banach spaces [J]. Journal of Southeast University (English Edition), 2008, 24 (4): 541-544. [doi:10.3969/j.issn.1003-7985.2008.04.029]

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Nonlocal controllability for semilinear problems in Banach spaces()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

24

Issue:

2008 4

Page:

541-544

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2008-12-30

Info

Title:

Nonlocal controllability for semilinear problems in Banach spaces

Author(s):

Xue Xingmei;  Lü Zhong

Department of Mathematics, Southeast University, Nanjing 210096, China

Keywords:

nonlocal problem;  nonlocal controllability;  mild solution;  completely continuous

PACS:

O175.15

DOI:

10.3969/j.issn.1003-7985.2008.04.029

Abstract:

If A:D(A)⊂X→X is a densely defined and closed linear operator, which generates a linear semigroup S(t)in Banach space X.The nonlocal controllability for the following nonlocal semilinear problems: u′(t)=Au(t)+Bx(t)+f(t, u(t)), 0≤t≤T with nonlocal initial condition u(0)=u_0+g0(u)is discussed in Banach space X.The results show that if semigroup S(t)is strongly continuous, the functions f and g are compact and the control B is bounded, then it is nonlocally controllable.The nonlocal controllability for the above nonlocal problem is also studied when B and W are unbounded and the semigroup S(t)is compact or strongly continuous. For illustration, a partial differential equation is worked out.

References:

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Memo

Memo:

Biography: Xue Xingmei(1964—), male, doctor, associate professor, xmxue@seu.edu.cn.
Foundation item: the National Natural Science Foundation of China(No.10674024).
Citation: Xue Xingmei, Lü Zhong.Nonlocal controllability for semilinear problems in Banach spaces[J].Journal of Southeast University(English Edition), 2008, 24(4):541-544.

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