[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(
)
Banach空间中半线性问题的非局部可控性
)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
- Banach空间中半线性问题的非局部可控性
- Author(s):
- Xue Xingmei; Lü Zhong
- Department of Mathematics, Southeast University, Nanjing 210096, China
- 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)=u0+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.
- 设A:D(A)⊂X→X是Banach空间X上的线性稠定的闭算子, 它是X上的强连续有界线性算子半群S(t)的无穷小生成元.对于Banach空间X中的含非局部初值条件u(0)=u0+g0(u)的半线性Cauchy问题:u′(t)=Au(t)+Bx(t)+f(t, u(t)), 在A生成的线性算子半群S(t)是非紧, 映射f和g满足一定的紧性条件, 控制算子B是有界线性算子时, 证明了该问题是非局部可控的.并分别在半群是紧或强连续的条件下, 证明了在控制算子B和W不是有界情形时上面的非局部Cauchy问题是非局部可控的.同时给出了在偏微分方程中的可控性问题的一个应用.
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.