scholarly journals On the Variational Stability of a Class of Nonlinear Parabolic Optimal Control Problems

1996 ◽  
Vol 15 (1) ◽  
pp. 245-262 ◽  
Author(s):  
Nikolaos Papageorgiou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Variational Stability ◽  
Nonlinear Parabolic ◽  
Parabolic Optimal Control

scholarly journals On the variational stability of a class of nonlinear parabolic optimal control problems

1997 ◽  
Vol 39 (1) ◽  
pp. 77-92
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Partial Differential Operator ◽  
Control Problems ◽  
Parametric Optimal Control ◽  
Nonlinear Parabolic ◽  
Optimal Value ◽  
Γ Convergence ◽  
Convergence Of Operators ◽  
Parabolic Optimal Control

AbstractIn this paper we study parametric optimal control problems governed by a nonlinear parabolic equation in divergence form. The parameter appears in all the data of the problem, including the partial differential operator. Using as tools the G-convergence of operators and the Γ-convergence of functionals, we show that the set-valued map of optimal pairs is upper semicontinuous with respect to the parameter and the optimal value function responds continuously to changes of the parameter. Finally in the case of semilinear systems we show that our framework can also incorporate systems with weakly convergent coefficients.

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