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 Mat. Sb., 2009, Volume 200, Number 3, Pages 119–146 (Mi msb5007)

This article is cited in 14 scientific papers (total in 14 papers)

Mosco convergence of integral functionals and its applications

A. A. Tolstonogov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

Abstract: Questions relating to the Mosco convergence of integral functionals defined on the space of square integrable functions taking values in a Hilbert space are investigated. The integrands of these functionals are time-dependent proper, convex, lower semicontinuous functions on the Hilbert space. The results obtained are applied to the analysis of the dependence on the parameter of solutions of evolution equations involving time-dependent subdifferential operators. For example a parabolic inclusion is considered, where the right-hand side contains a sum of the $p$-Laplacian and the subdifferential of the indicator function of a time-dependent closed convex set. The convergence as $p\to+\infty$ of solutions of this inclusion is investigated.
Bibliography: 20 titles.

Keywords: Mosco convergence, integral functionals, $p$-Laplacian.

DOI: https://doi.org/10.4213/sm5007

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English version:
Sbornik: Mathematics, 2009, 200:3, 429–454

Bibliographic databases:

UDC: 517.987.4
MSC: 34G25, 45P05
Received: 26.03.2008 and 03.12.2008

Citation: A. A. Tolstonogov, “Mosco convergence of integral functionals and its applications”, Mat. Sb., 200:3 (2009), 119–146; Sb. Math., 200:3 (2009), 429–454

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. A. Tolstonogov, “Variational stability of optimal control problems involving subdifferential operators”, Sb. Math., 202:4 (2011), 583–619
2. Timoshin S.A., Tolstonogov A.A., “Existence and properties of solutions of a control system with hysteresis effect”, Nonlinear Anal., 74:13 (2011), 4433–4447
3. Tolstonogov A.A., “Continuity in the parameter of the minimum value of an integral functional over the solutions of an evolution control system”, Nonlinear Anal., 75:12 (2012), 4711–4727
4. Bocea M., Mihăilescu M., Pérez-Llanos M., Rossi J.D., “Models for growth of heterogeneous sandpiles via Mosco convergence”, Asymptotic Anal., 78:1-2 (2012), 11–36
5. S. A. Timoshin, “Variational stability of some optimal control problems describing hysteresis effects”, SIAM J. Control Optim., 52:4 (2014), 2348–2370
6. A. A. Tolstonogov, “Compactness in the space of set-valued mappings with closed values”, Dokl. Math., 89:3 (2014), 293–295
7. Timoshin S.A., “Control system with hysteresis and delay”, Syst. Control Lett., 91 (2016), 43–47
8. Timoshin S.A., “A relaxation result for unbounded control system with hysteresis”, J. Math. Anal. Appl., 435:2 (2016), 1036–1053
9. Krejci P., Timoshin S.A., “Coupled ODEs Control System with Unbounded Hysteresis Region”, SIAM J. Control Optim., 54:4 (2016), 1934–1949
10. Tolstonogov A.A., “Existence and relaxation of solutions for a subdifferential inclusion with unbounded perturbation”, J. Math. Anal. Appl., 447:1 (2017), 269–288
11. Timoshin S.A., “Existence and Relaxation For Subdifferential Inclusions With Unbounded Perturbation”, Math. Program., 166:1-2 (2017), 65–85
12. Timoshin S.A., “Bang-Bang Control of a Thermostat With Nonconstant Cooling Power”, ESAIM-Control OPtim. Calc. Var., 24:2 (2018), 709–719
13. Tolstonogov A.A., “Filippov-Wazewski Theorem For Subdifferential Inclusions With An Unbounded Perturbation”, SIAM J. Control Optim., 56:4 (2018), 2878–2900
14. A. A. Tolstonogov, “Teorema N. N. Bogolyubova dlya upravlyaemoi sistemy, svyazannoi s variatsionnym neravenstvom”, Izv. RAN. Ser. matem., 84:6 (2020), 165–196
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