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→+∞ of solutions of this inclusion is investigated.
Bibliography: 20 titles.
Keywords:
Mosco convergence, integral functionals, p-Laplacian.
\Bibitem{Tol09}
\by A.~A.~Tolstonogov
\paper Mosco convergence of integral functionals and its applications
\jour Sb. Math.
\yr 2009
\vol 200
\issue 3
\pages 429--454
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Linking options:
https://www.mathnet.ru/eng/sm5007
https://doi.org/10.1070/SM2009v200n03ABEH004003
https://www.mathnet.ru/eng/sm/v200/i3/p119
This publication is cited in the following 16 articles:
Boccardo L., “Some New Results About Mosco Convergence”, J. Convex Anal., 28:2 (2021), 387–394
A. A. Tolstonogov, “Bogolyubov's theorem for a controlled system related to a variational inequality”, Izv. Math., 84:6 (2020), 1192–1223
A. A. Tolstonogov, “Polyhedral multivalued mappings: properties and applications”, Siberian Math. J., 61:2 (2020), 338–358
Timoshin S.A., “Bang-Bang Control of a Thermostat With Nonconstant Cooling Power”, ESAIM-Control OPtim. Calc. Var., 24:2 (2018), 709–719
Tolstonogov A.A., “Filippov-Wazewski Theorem For Subdifferential Inclusions With An Unbounded Perturbation”, SIAM J. Control Optim., 56:4 (2018), 2878–2900
Tolstonogov A.A., “Existence and relaxation of solutions for a subdifferential inclusion with unbounded perturbation”, J. Math. Anal. Appl., 447:1 (2017), 269–288
Timoshin S.A., “Existence and Relaxation For Subdifferential Inclusions With Unbounded Perturbation”, Math. Program., 166:1-2 (2017), 65–85
Timoshin S.A., “Control system with hysteresis and delay”, Syst. Control Lett., 91 (2016), 43–47
Timoshin S.A., “A relaxation result for unbounded control system with hysteresis”, J. Math. Anal. Appl., 435:2 (2016), 1036–1053
Krejci P., Timoshin S.A., “Coupled ODEs Control System with Unbounded Hysteresis Region”, SIAM J. Control Optim., 54:4 (2016), 1934–1949
S. A. Timoshin, “Variational stability of some optimal control problems describing hysteresis effects”, SIAM J. Control Optim., 52:4 (2014), 2348–2370
A. A. Tolstonogov, “Compactness in the space of set-valued mappings with closed values”, Dokl. Math., 89:3 (2014), 293–295
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
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
A. A. Tolstonogov, “Variational stability of optimal control problems involving subdifferential operators”, Sb. Math., 202:4 (2011), 583–619
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
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