UNIFORM ATTRACTORS IN SUP-NORM FOR SEMI LINEAR PARABOLIC PROBLEM AND APPLICATION TO THE ROBUST STABILITY THEORY

被引：0

作者：

Kapustyan, Oleksiy ^{[1
]}

Kapustian, Olena ^{[2
,3
]}

Stanzytskyi, Oleksandr ^{[4
]}

Korol, Ihor ^{[5
,6
]}

机构：

[1] Taras Shevchenko Natl Univ Kyiv, Mech & Math Fac, Dept Integral & Differential Equat, Volodymyrska St, 60, UA-01601 Kiev, Ukraine

[2] Taras Shevchenko Natl Univ Kyiv, Fac Comp Sci & Cybernet, Dept Syst Anal & Decis Making Theory, Volodymyrska St, 60, UA-01601 Kiev, Ukraine

[3] Univ Aquila, Dipartimento Ingn & Sci Informaz & Matemat, Via Vetorio, Coppito 1, I-67100 Laquila, Italy

[4] Taras Shevchenko Natl Univ Kyiv, Mech & Math Fac, Dept Gen Math, Volodymyrska St, 60, UA-01601 Kiev, Ukraine

[5] Uzhgorod Natl Univ, Fac Math & Digital Technol, Dept Algebra & Differential Equat, Narodna Sq, 3, UA-88000 Uzhgorod, Ukraine

[6] John Paul II Catholic Univ Lublin, Fac Nat Sci & Hlth, Dept Math Anal, Al Raclawickie 14, PL-20950 Lublin, Poland

来源：

ARCHIVUM MATHEMATICUM | 2023年 / 59卷 / 03期

关键词：

parabolic equations; attractor; stability;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we establish the existence of the uniform attractor for a semi linear parabolic problem with bounded non autonomous disturbances in the phase space of continuous functions. We applied obtained results to prove the asymptotic gain property with respect to the global attractor of the undisturbed system.

引用

页码：191 / 200

页数：10

共 26 条

[1] Asrorov F., 2019, East.-Eur. J. Enterp. Technol, V6, P14
[2] Barabash Oleg, 2019, 2019 IEEE 5th International Conference Actual Problems of Unmanned Aerial Vehicles Developments (APUAVD), P136
[3] Chepyzkov V.V., 2002, Attractors for equations of mathematical physics, V49
[4] A local input-to-state stability result w.r.t. attractors of nonlinear reaction-diffusion equations
Dashkovskiy, Sergey
Kapustyan, Oleksiy
Schmid, Jochen
[J]. MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2020, 32 (03) : 309 - 326
[5] Invariance and stability of global attractors for multi-valued impulsive dynamical systems
Dashkovskiy, Sergey
Feketa, Petro
Kapustyan, Oleksiy
Romaniuk, Iryna
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 458 (01) : 193 - 218
[6] GLOBAL ATTRACTORS OF IMPULSIVE PARABOLIC INCLUSIONS
Dashkovskiy, Sergey
Kapustyan, Oleksiy
Romaniuk, Iryna
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2017, 22 (05): : 1875 - 1886
[7] Input-to-state stability of infinite-dimensional control systems
Dashkovskiy, Sergey
Mironchenko, Andrii
[J]. MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2013, 25 (01) : 1 - 35
[8] Gorban N.V., 2015, J. Automat. Inform. Sci., V47, P48
[9] Haraux A., 1983, Ann. Fac Sci. Toulouse Math., V5, P265
[10] Kapustyan O.V., 2015, Appl. Math. Inform. Sci., V9, P2257

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