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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

Full text: PDF file (659 kB)
References: PDF file   HTML file

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

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  • http://mi.mathnet.ru/eng/msb/v200/i3/p119

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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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    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  crossref  mathscinet  zmath  isi  elib  scopus
    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  crossref  mathscinet  zmath  isi  elib  scopus
    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  crossref  mathscinet  zmath  isi  elib  scopus
    5. S. A. Timoshin, “Variational stability of some optimal control problems describing hysteresis effects”, SIAM J. Control Optim., 52:4 (2014), 2348–2370  crossref  mathscinet  zmath  isi  elib  scopus
    6. A. A. Tolstonogov, “Compactness in the space of set-valued mappings with closed values”, Dokl. Math., 89:3 (2014), 293–295  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    7. Timoshin S.A., “Control system with hysteresis and delay”, Syst. Control Lett., 91 (2016), 43–47  crossref  mathscinet  zmath  isi  scopus
    8. Timoshin S.A., “A relaxation result for unbounded control system with hysteresis”, J. Math. Anal. Appl., 435:2 (2016), 1036–1053  crossref  mathscinet  zmath  isi  scopus
    9. Krejci P., Timoshin S.A., “Coupled ODEs Control System with Unbounded Hysteresis Region”, SIAM J. Control Optim., 54:4 (2016), 1934–1949  crossref  mathscinet  zmath  isi  scopus
    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  crossref  mathscinet  zmath  isi  scopus
    11. Timoshin S.A., “Existence and Relaxation For Subdifferential Inclusions With Unbounded Perturbation”, Math. Program., 166:1-2 (2017), 65–85  crossref  mathscinet  zmath  isi  scopus
    12. Timoshin S.A., “Bang-Bang Control of a Thermostat With Nonconstant Cooling Power”, ESAIM-Control OPtim. Calc. Var., 24:2 (2018), 709–719  crossref  mathscinet  zmath  isi  scopus
    13. Tolstonogov A.A., “Filippov-Wazewski Theorem For Subdifferential Inclusions With An Unbounded Perturbation”, SIAM J. Control Optim., 56:4 (2018), 2878–2900  crossref  mathscinet  zmath  isi  scopus
    14. A. A. Tolstonogov, “Teorema N. N. Bogolyubova dlya upravlyaemoi sistemy, svyazannoi s variatsionnym neravenstvom”, Izv. RAN. Ser. matem., 84:6 (2020), 165–196  mathnet  crossref
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