Nonlinear Semigroups for Delay Equations in Hilbert Spaces, Inertial Manifolds and Dimension Estimates

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Nonlinear Semigroups for Delay Equations in Hilbert Spaces, Inertial Manifolds and Dimension Estimates. / Anikushin, Mikhail .

In: Differencialnie Uravnenia i Protsesy Upravlenia, No. 4, 2022.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{cf6b80caff674355a461f9f684781348,

title = "Nonlinear Semigroups for Delay Equations in Hilbert Spaces, Inertial Manifolds and Dimension Estimates",

abstract = "We study the well-posedness of nonautonomous nonlinear delay equations in Rnas evolutionary equations in a proper Hilbert space. We present aconstruction of solving operators (nonautonomous case) or nonlinear semigroups(autonomous case) for a large class of such equations. The main idea can beeasily extended for certain PDEs with delay. Our approach has lesser limitationsand much more elementary than some previously known constructions of suchsemigroups and solving operators based on the theory of accretive operators. Inthe autonomous case we also study dierentiability properties of these semigroupsin order to apply various dimension estimates using the Hilbert space geometry.However, obtaining eective dimension estimates for delay equations is a nontrivial problem and we explain it by means of a scalar delay equation. We also discussour adjacent results concerned with inertial manifolds and their construction fordelay equations.",

keywords = "Delay equations, Nonlinear semigroups, Inertial manifolds, Dimension estimates",

author = "Mikhail Anikushin",

year = "2022",

language = "English",

journal = "ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ",

issn = "1817-2172",

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

number = "4",

}

RIS

TY - JOUR

T1 - Nonlinear Semigroups for Delay Equations in Hilbert Spaces, Inertial Manifolds and Dimension Estimates

AU - Anikushin, Mikhail

PY - 2022

Y1 - 2022

N2 - We study the well-posedness of nonautonomous nonlinear delay equations in Rnas evolutionary equations in a proper Hilbert space. We present aconstruction of solving operators (nonautonomous case) or nonlinear semigroups(autonomous case) for a large class of such equations. The main idea can beeasily extended for certain PDEs with delay. Our approach has lesser limitationsand much more elementary than some previously known constructions of suchsemigroups and solving operators based on the theory of accretive operators. Inthe autonomous case we also study dierentiability properties of these semigroupsin order to apply various dimension estimates using the Hilbert space geometry.However, obtaining eective dimension estimates for delay equations is a nontrivial problem and we explain it by means of a scalar delay equation. We also discussour adjacent results concerned with inertial manifolds and their construction fordelay equations.

AB - We study the well-posedness of nonautonomous nonlinear delay equations in Rnas evolutionary equations in a proper Hilbert space. We present aconstruction of solving operators (nonautonomous case) or nonlinear semigroups(autonomous case) for a large class of such equations. The main idea can beeasily extended for certain PDEs with delay. Our approach has lesser limitationsand much more elementary than some previously known constructions of suchsemigroups and solving operators based on the theory of accretive operators. Inthe autonomous case we also study dierentiability properties of these semigroupsin order to apply various dimension estimates using the Hilbert space geometry.However, obtaining eective dimension estimates for delay equations is a nontrivial problem and we explain it by means of a scalar delay equation. We also discussour adjacent results concerned with inertial manifolds and their construction fordelay equations.

KW - Delay equations

KW - Nonlinear semigroups

KW - Inertial manifolds

KW - Dimension estimates

M3 - Article

JO - ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1817-2172

IS - 4

ER -

ID: 105233445