Optimal Obstacle Control Problem

ZHU Li; LI Xiu-hua; GOU Xing-ming

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Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(5): 505-514

ZHU Li, LI Xiu-hua, GOU Xing-ming. Optimal Obstacle Control Problem[J]. Applied Mathematics and Mechanics, 2008, 29(5): 505-514.

Citation:

ZHU Li, LI Xiu-hua, GOU Xing-ming. Optimal Obstacle Control Problem[J]. Applied Mathematics and Mechanics, 2008, 29(5): 505-514.

Citation:

ZHU Li, LI Xiu-hua, GOU Xing-ming. Optimal Obstacle Control Problem[J]. Applied Mathematics and Mechanics, 2008, 29(5): 505-514.

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Optimal Obstacle Control Problem

1.
Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, P. R. China;

Received Date: 2007-08-15
Rev Recd Date: 2008-04-14
Publish Date: 2008-05-15

Abstract

Abstract

Some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality was discussed,and the existence,uniqueness and regularity of the optimal control problem were established.In addition,the approximate problem of the optimal obstacle problem also was studied.
- obstacle problem,
- penalized method,
- optimality system,
- approximate problem

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References(15)

References

[1]	Adams D R,Lenhart S. An obstacle control problem with a source term[J].Appl Math Optim,2008,47(1):79-95.
[2]	Adams D R, Lenhart S. Optimal control of the obstacle for a parabolic variational inequality[J].J Math Anal Appl,2002,268:602-614. doi: 10.1006/jmaa.2001.7833
[3]	Adams D R, Lenhart S, Yong J.Optimal control of the obstacle for an elliptic variational inequality[J].Appl Math Optim,1998,38:121-140. doi: 10.1007/s002459900085
[4]	Barbu V.Analysis and Control of Nonlinear Infinite Dimensional Systems[M].Math Sci Engrg. 190. San Diego :Academic Press, 1993.
[5]	Chen Q. Indirect obstacle control problem for semilinear elliptic variational inequalities[J].SIAM J Control Optim,1999,38:138-158. doi: 10.1137/S0363012998343379
[6]	LOU Hong-wei.An optimal control problem governed by quasi-linear variational inequalities[J].SIAM J Control Optim,2003,41(4): 1229-1253.
[7]	Chen Q. Optimal control for semilinear evolutionary variational bilateral problems[J].J Math Anal Appl,2003,277(1):303-323. doi: 10.1016/S0022-247X(02)00569-3
[8]	Duvaunt G, Lions J L.Les Inequations en Mecanique et en Pysique[M].Paris:Dunod,1972.
[9]	Bergounioux M, Kunisch K.Augmented Lagrangian techniques for elliptic state constrained optimal control problems[J].SIAM J Control Optim,1997,35:1524-1543. doi: 10.1137/S036301299529330X
[10]	Bergounioux M. Optimal control of semilinear elliptic obstacle problems[J].J Nonlinear Convex Anal,2002,3(1):25-39.
[11]	Chipot M.Variational Inequalities and Flow in Porous Media[M].New York:Springer-Verlag,1984.
[12]	Bergounioux M, Lenhart S. Optimal control of bilateral obstacle problems[J].SIAM J Control Optim,2004,43(1):240-255. doi: 10.1137/S0363012902416912
[13]	Bucur D, Buttazzo G,Trabeschi P. An existence result for optimal obstacles[J].J Funct Anal,1999,162(1):96-119. doi: 10.1006/jfan.1998.3363
[14]	Buttazzo G, Wagner A. On the optimal shape of a rigid body supported by an elastic membrane[J].Nonlinear Anal,2000,39(1):47-63. doi: 10.1016/S0362-546X(98)00163-1
[15]	张恭庆，林源渠.泛函分析讲义[M].北京：北京大学出版社，2003，85.