Nonexistence and Existence of an Optimal Control Problem Governed by a Class of Semilinear Elliptic Equations

被引:0
作者
Shu Luan
机构
[1] Zhanjiang Normal College,School of Mathematics and Computation
来源
Journal of Optimization Theory and Applications | 2013年 / 158卷
关键词
Optimal control; Semilinear elliptic equations; Nonexistence; Existence; Relaxed control;
D O I
暂无
中图分类号
学科分类号
摘要
An optimal control problem governed by a class of semilinear elliptic equations is considered in this paper. Using relaxed controls, the nonexistence and existence results of an optimal control are obtained.
引用
收藏
页码:1 / 10
页数:9
相关论文
共 23 条
[1]  
Young L.C.(1937)Generalized curves and the existence of an attained absolute minimum in the calculus of variations C. R. Sci. Lett. Varsovie, C. III 30 212-234
[2]  
McShane E.J.(1940)Generalized curves Duke Math. J. 6 513-536
[3]  
Lou H.(2003)Existence of optimal controls for semilinear elliptic equations without Cesari-type conditions ANZIAM J. 45 115-131
[4]  
Lou H.(2003)Existence of optimal controls for semilinear parabolic equations without Cesari-type conditions Appl. Math. Optim. 47 121-142
[5]  
Lou H.(2005)Existence of optimal controls in the absence of Cesari-type conditions for semilinear elliptic and parabolic systems J. Optim. Theory Appl. 125 367-391
[6]  
Lou H.(2009)Analysis of the optimal relaxed control to an optimal control problem Appl. Math. Optim. 59 75-97
[7]  
Neustadt L.W.(1963)The existence of optimal controls in the absence of convexity conditions J. Math. Anal. Appl. 7 110-117
[8]  
Artstein Z.(1974)On a variational problem J. Math. Anal. Appl. 45 405-415
[9]  
Balder E.J.(1994)New existence results for optimal controls in the absence of convexity: the importance of extremality SIAM J. Control Optim. 32 890-916
[10]  
Cellina A A.(1990)On a classical problem of the calculus of variations without convexity assumptions Ann. Inst. Henri Poincaré, Anal. Non Linéaire 7 97-106