GLOBAL ATTRACTORS AND ASYMPTOTIC GAIN PROPERTY FOR NON-AUTONOMOUS INCLUSION OF REACTION-DIFFUSION TYPE

Kapustyan O.V. Yusypiv T.V. Ospanov M. Alday M.
June 2025 Oles Honchar Dnipro National University

Journal of Optimization, Differential Equations and their Applications
2025 #33 Issue 1 1 - 14 pp.

We investigate global resolvability and stability of attractors for parabolic inclusion with multi-valued interaction function of reaction-diffusion type and non-autonomous disturbances. For the class of L²-disturbances, we prove existence of global solutions in the phase space L². In the class of translation-bounded disturbances we prove that obtained global solutions generate the family of multi-valued semiprocesses which possesses a uniform attractor. Finally, for L^∞-disturbances we show that the global attractor of unperturbed system is stable w.r.t. disturbances in the asymptotic gain sense.

asymptotic gain , parabolic inclusion , reaction-diffusion , stability , uniform attractor

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Taras Shevchenko National University of Kyiv, Volodymyrska Street 64, Kyiv, 01601, Ukraine
L.N. Gumilyov Eurasian National University, Satpayev str., 2, Astana, 010000, Kazakhstan

Taras Shevchenko National University of Kyiv
L.N. Gumilyov Eurasian National University

10 лет помогаем публиковать статьи Международный издатель

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