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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On parametric evolution inclusions of the subdifferential type with applications to optimal control problems


Author: Nikolaos S. Papageorgiou
Journal: Trans. Amer. Math. Soc. 347 (1995), 203-231
MSC: Primary 49J24; Secondary 34A60, 34G20, 49K40
MathSciNet review: 1282896
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Abstract: In this paper we study parametric evolution inclusions of the subdifferential type and their applications to the sensitivity analysis of nonlinear, infinite dimensional optimal control problems. The parameter appears in all the data of the problem, including the subdifferential operator. First we establish several continuity results for the solution multifunction of the subdifferential inclusion. Then we study how these results can be used to examine the sensitivity properties (variational stability) of certain broad classes of nonlinear infinite dimensional optimal control problems. Some examples are worked out in detail, illustrating the applicability of our work. These include obstacle problems (with time varying obstacles), optimal control of distributed parameter systems, and differential variational inequalities.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1282896-X
PII: S 0002-9947(1995)1282896-X
Keywords: Subdifferential, strong solution, $ G$-convergence, Mosco convergence, Vietoris topology, Hausdorff metric, optimal control problem, obstacle problem, differential variational inequality
Article copyright: © Copyright 1995 American Mathematical Society



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