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
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topKandilakis, 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
top- Aubin J.-P., Cellina A., Differential Inclusions, Springer, Berlin, 1983. Zbl0538.34007MR0755330
- Barbu V., Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff International Publishing, Leiden, The Netherlands, 1976. Zbl0328.47035MR0390843
- Brezis H., Operateurs Maximaux Monotones, North Holland, Amsterdam, 1973. Zbl0252.47055
- DeBlasi F., Myjak J., On continuous approximations for multifunctions, Pacific J. Math. 123 (1986), 9-31. (1986) MR0834135
- Hiai F., Umgaki H., Integrals, conditional expectations and martingales of multivalued functions, J. Multiv. Anal. 7 (1977), 149-182. (1977) MR0507504
- Klein E., Thompson A., Theory of Correspondences, Wiley, New York, 1984. Zbl0556.28012MR0752692
- Lim T.-C., On fixed point stability for set-valued contractive mappings with applications to generalized differential equations, J. Math. Anal. Appl. 110 (1985), 436-441. (1985) Zbl0593.47056MR0805266
- Nadler S.B., Multivalued contraction mappings, Pacific J. Math. 30 (1969), 475-488. (1969) MR0254828
- Papageorgiou N.S., A stability result for differential m inclusions in Banach spaces, J. Math. Anal. Appl. 118 (1986), 232-246. (1986) MR0849457
- Papageorgiou N.S., Convergence theorems for Banach space valued integrable multifunctions, International J. Math. and Math. Sci. 10 (1987), 433-442. (1987) Zbl0619.28009MR0896595
- Papageorgiou N.S., On measurable multifunctions with applications to random multivalued equations, Math. Japonica 34 (1989), 287-296. (1989)
- Papageorgiou N.S., Infinite dimensional control systems with state and control constraints, Proceedings of the Indian Academy of Sciences 100 (1990), 65-77. (1990) Zbl0703.49018MR1051092
- Papageorgiou N.S., On evolution inclusions associated with time dependent convex subdifferentials, Comment. Math. Univ. Carolinae 31 (1990), 517-527. (1990) Zbl0711.34076MR1078486
- Przyluski K.M., Remarks on continuous dependence of an optimal control on parameters, in: Game Theory and Mathematical Economics, eds. O. Moeschlin and D. Pallashke, North Holland, Amsterdam, 1981, pp. 331-327. Zbl0475.49025
- Rybinski L., A fixed point approach in the study of the solution sets of Lipschitzian functional-differential inclusions, J. Math. Anal. Appl. 160 (1991), 24-46. (1991) Zbl0735.34016MR1124074
- Stassinopoulos G., Vinter R., Continuous dependence of a differential inclusion on the right-hand side with applications to stability of optimal control problems, SIAM J. Control and Optim. 17 (1979), 432-449. (1979) MR0528904
- Tolstonogov A., On the dependence on parameter of a solution of a differential inclusion with nonconvex second member, Diff. Equations 18 (1982), 1105-1113. (1982) MR0672160
- Tsukada M., Convergence of best approximations in smooth Banach spaces, J. Approx. Theory 40 (1984), 301-309. (1984) MR0740641
- Vasilev A., Continuous dependence of the solutions of differential inclusions on the parameter, Ukrainian Math. J. 35 (1983), 520-524. (1983) MR0723122
- Wagner D., Survey of measurable selection theorems, SIAM J. Control Optim. 15 (1977), 859-903. (1977) Zbl0407.28006MR0486391
- Watanabe J., On certain nonlinear evolution equations, J. Math. Soc. Japan 25 (1973), 446-463. (1973) Zbl0253.35053MR0326522
- Yamada Y., On evolution inclusions generated by subdifferential operators, J. Fac. Sci. Univ. Tokyo 23 (1976), 491-515. (1976) MR0425701
- Yotsutani S., Evolution equations associated with the subdifferentials, J. Math. Soc. Japan 31 (1978), 623-646. (1978) Zbl0405.35043MR0544681
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