Почти автоморфная динамика в почти периодических коциклах с одномерным инерциальным многообразием

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Почти автоморфная динамика в почти периодических коциклах с одномерным инерциальным многообразием. / Anikushin, Mikhail.

в: Differencialnie Uravnenia i Protsesy Upravlenia, Том 2021, № 2, 2021, стр. 13-48.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{b49769a7ffef4a8ea3b4aca71432e619,

title = "Почти автоморфная динамика в почти периодических коциклах с одномерным инерциальным многообразием",

abstract = "We study ω-limit and minimal sets of skew-product semiflows associated with cocycles in Banach spaces, which admit one-dimensional inertial manifolds. Our main aim is to extend for such cocycles classical results of W. Shen and Y. Yi on almost automorphy of minimal sets arising in the case of scalar almost periodic ODEs and scalar almost periodic parabolic equations in one-dimensional domains. We give applications for ODEs, delay equations and semilinear parabolic equations. Conditions for the existence of inertial manifolds are given in our adjacent works. In applications, these conditions are verified with the aid of recently obtained versions of the Frequency Theorem.",

keywords = "Almost automorphic solution, Almost periodic cocycle, Frequency theorem, Inertial manifold",

author = "Mikhail Anikushin",

note = "Funding Information: Acknowledgments. The reported study was funded by RFBR, project number 20-31-90008; by a grant in the subsidies form from the federal budget for the creation and development of international world-class math centers, agreement between MES RF and PDMI RAS No. 075-15-2019-1620; by V. A. Rokhlin grant for young mathematicians of St. Petersburg. Publisher Copyright: {\textcopyright} 2021 Saint-Petersburg State University. All rights reserved.",

year = "2021",

language = "русский",

volume = "2021",

pages = "13--48",

journal = "ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ",

issn = "1817-2172",

publisher = "Электронный журнал {"}Дифференциальные уравнения и процессы управления{"}",

number = "2",

}

RIS

TY - JOUR

T1 - Почти автоморфная динамика в почти периодических коциклах с одномерным инерциальным многообразием

AU - Anikushin, Mikhail

N1 - Funding Information: Acknowledgments. The reported study was funded by RFBR, project number 20-31-90008; by a grant in the subsidies form from the federal budget for the creation and development of international world-class math centers, agreement between MES RF and PDMI RAS No. 075-15-2019-1620; by V. A. Rokhlin grant for young mathematicians of St. Petersburg. Publisher Copyright: © 2021 Saint-Petersburg State University. All rights reserved.

PY - 2021

Y1 - 2021

N2 - We study ω-limit and minimal sets of skew-product semiflows associated with cocycles in Banach spaces, which admit one-dimensional inertial manifolds. Our main aim is to extend for such cocycles classical results of W. Shen and Y. Yi on almost automorphy of minimal sets arising in the case of scalar almost periodic ODEs and scalar almost periodic parabolic equations in one-dimensional domains. We give applications for ODEs, delay equations and semilinear parabolic equations. Conditions for the existence of inertial manifolds are given in our adjacent works. In applications, these conditions are verified with the aid of recently obtained versions of the Frequency Theorem.

AB - We study ω-limit and minimal sets of skew-product semiflows associated with cocycles in Banach spaces, which admit one-dimensional inertial manifolds. Our main aim is to extend for such cocycles classical results of W. Shen and Y. Yi on almost automorphy of minimal sets arising in the case of scalar almost periodic ODEs and scalar almost periodic parabolic equations in one-dimensional domains. We give applications for ODEs, delay equations and semilinear parabolic equations. Conditions for the existence of inertial manifolds are given in our adjacent works. In applications, these conditions are verified with the aid of recently obtained versions of the Frequency Theorem.

KW - Almost automorphic solution

KW - Almost periodic cocycle

KW - Frequency theorem

KW - Inertial manifold

UR - http://www.scopus.com/inward/record.url?scp=85108733219&partnerID=8YFLogxK

M3 - статья

AN - SCOPUS:85108733219

VL - 2021

SP - 13

EP - 48

JO - ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1817-2172

IS - 2

ER -

ID: 86300536