Evolution inclusions of the subdifferential type depending on a parameter

Dimitrios A. Kandilakis; Nikolaos S. Papageorgiou

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 3, page 437-449
  • ISSN: 0010-2628

Abstract

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In this paper we study evolution inclusions generated by time dependent convex subdifferentials, with the orientor field F depending on a parameter. Under reasonable hypotheses on the data, we show that the solution set S ( λ ) is both Vietoris and Hausdorff metric continuous in λ Λ . Using these results, we study the variational stability of a class of nonlinear parabolic optimal control problems.

How to cite

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Kandilakis, Dimitrios A., and Papageorgiou, Nikolaos S.. "Evolution inclusions of the subdifferential type depending on a parameter." Commentationes Mathematicae Universitatis Carolinae 33.3 (1992): 437-449. <http://eudml.org/doc/21872>.

@article{Kandilakis1992,
abstract = {In this paper we study evolution inclusions generated by time dependent convex subdifferentials, with the orientor field $F$ depending on a parameter. Under reasonable hypotheses on the data, we show that the solution set $S(\lambda )$ is both Vietoris and Hausdorff metric continuous in $\lambda \in \Lambda $. Using these results, we study the variational stability of a class of nonlinear parabolic optimal control problems.},
author = {Kandilakis, Dimitrios A., Papageorgiou, Nikolaos S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {subdifferential; compact type; Vietoris topology; Hausdorff metric; parabolic optimal control problem; evolution; time dependent convex subdifferentials; orientor field; variational stability; nonlinear parabolic optimal control problems},
language = {eng},
number = {3},
pages = {437-449},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Evolution inclusions of the subdifferential type depending on a parameter},
url = {http://eudml.org/doc/21872},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Kandilakis, Dimitrios A.
AU - Papageorgiou, Nikolaos S.
TI - Evolution inclusions of the subdifferential type depending on a parameter
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 3
SP - 437
EP - 449
AB - In this paper we study evolution inclusions generated by time dependent convex subdifferentials, with the orientor field $F$ depending on a parameter. Under reasonable hypotheses on the data, we show that the solution set $S(\lambda )$ is both Vietoris and Hausdorff metric continuous in $\lambda \in \Lambda $. Using these results, we study the variational stability of a class of nonlinear parabolic optimal control problems.
LA - eng
KW - subdifferential; compact type; Vietoris topology; Hausdorff metric; parabolic optimal control problem; evolution; time dependent convex subdifferentials; orientor field; variational stability; nonlinear parabolic optimal control problems
UR - http://eudml.org/doc/21872
ER -

References

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