Zobrazeno 1 - 10
of 54
pro vyhledávání: '"Oleksiy V. Kapustyan"'
Publikováno v:
Journal of Optimization, Differential Equations and Their Applications, Vol 31, Iss 1, Pp 111-124 (2023)
The paper investigates the issue of stability with respect to external disturbances for the global attractor of the wave equation under conditions that do not ensure the uniqueness of the solution to the initial problem. Under general conditions for
Externí odkaz:
https://doaj.org/article/6189d51e5d924643b0d174aa4ea8a5ee
Publikováno v:
Journal of Optimization, Differential Equations and Their Applications, Vol 30, Iss 2, Pp 49-61 (2022)
We establish the local input-to-state stability of multi-valued evolutionary systems with bounded disturbances with respect to the global attractor of the respective undisturbed system. We apply obtained results to disturbed reaction-diffusion equati
Externí odkaz:
https://doaj.org/article/c2bf6959205e4cea8166542e5bf99fed
Autor:
Nataliia V. Gorban, Oleksiy V. Kapustyan, Pavlo O. Kasyanov, Olha V. Khomenko, Liliia S. Paliichuk, Jose Valero, Michael Z. Zgurovsky
Publikováno v:
Journal of Optimization, Differential Equations and Their Applications, Vol 26, Iss 2, Pp 1-12 (2018)
In this paper we prove the existence of uniform global attractors in the strong topology of the phase space for semiflows generated by vanishing viscosity approximations of some class of non-autonomous complex fluids.
Externí odkaz:
https://doaj.org/article/7d4961218a2e4c9faca1e92214007f33
Publikováno v:
Axioms, Vol 11, Iss 4, p 175 (2022)
In this paper, we use the averaging method to find an approximate solution in the optimal control problem of a parabolic system with non-linearity of the form f(t/ε,y) on an infinite time interval.
Externí odkaz:
https://doaj.org/article/d16d0fd799c8439f950ce4810837cf53
Publikováno v:
Mathematical Problems in Engineering, Vol 2021 (2021)
In this paper, we develop a general approach to investigate limit dynamics of infinite-dimensional dissipative impulsive systems whose initial conditions do not uniquely determine their long time behavior. Based on the notion of an uniform attractor,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c65c2f8b9c7d72f49929dd316958f89f
https://doi.org/10.1155/2021/7385450
https://doi.org/10.1155/2021/7385450
Publikováno v:
System research and information technologies. :140-148
The authors consider the pulsed dynamical systems generated by evolutionary processes. The trajectories of these processes undergo the pulsed perturbation when the energy functional reaches some fixed limit value. The generalization of the classical
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::880a6d360a44adc22b5abd9c57274e51
https://doi.org/10.20535/srit.2308-8893.2021.2.11
https://doi.org/10.20535/srit.2308-8893.2021.2.11
Publikováno v:
Journal of Mathematical Sciences. 254:219-228
We consider a weakly nonlinear N-dimensional parabolic system whose solutions are subjected to impulsive perturbations upon attainment of a certain fixed subset in the phase space. For broad classes of impulsive perturbations, it is proved that the s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ab6654bc8bc495466964b9880ab5729c
https://doi.org/10.1007/s10958-021-05299-1
https://doi.org/10.1007/s10958-021-05299-1
Publikováno v:
Mathematics of Control, Signals, and Systems. 32:309-326
We establish the local input-to-state stability of a large class of disturbed nonlinear reaction–diffusion equations w.r.t. the global attractor of the respective undisturbed system.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::13342f5f61fe8427d49c70a730acb42b
https://doi.org/10.1007/s00498-020-00256-w
https://doi.org/10.1007/s00498-020-00256-w
Publikováno v:
IFAC-PapersOnLine. 53:3186-3191
We establish local input-to-state stability and asymptotic gain results for a class of nonlinear infinite-dimensional systems with respect to the global attractor of the respective undisturbed system. We apply our results to a large class of reaction
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0fe855d1bbdb10162689e7a955a11d7d
https://doi.org/10.1016/j.ifacol.2020.12.2536
https://doi.org/10.1016/j.ifacol.2020.12.2536
Publikováno v:
IFAC-PapersOnLine. 53:3180-3185
In this paper we investigate stability of uniformly attracting sets for semiflows generated by impulsive infinite-dimensional dynamical systems without uniqueness. Obtained abstract results are applied to weakly nonlinear parabolic system, whose traj
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9bb98c8dfae63ae26519049b791b7554
https://doi.org/10.1016/j.ifacol.2020.12.2534
https://doi.org/10.1016/j.ifacol.2020.12.2534