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Around Ovsyannikov's method

Dmitri Finkelshtein Orcid Logo

Methods of Functional Analysis and Topology, Volume: 21, Issue: 2, Pages: 134 - 150

Swansea University Author: Dmitri Finkelshtein Orcid Logo

Abstract

We study existence, uniqueness, and a limiting behaviour of solutions to an abstract linear evolution equation in a scale of Banach spaces. The generator of the equation is a perturbation of the operator which satisfies the classical assumptions of Ovsyannikov's method by a generator of a $C_0$...

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Published in: Methods of Functional Analysis and Topology
Published: 2015
Online Access: http://www.imath.kiev.ua/~mfat/
URI: https://cronfa.swan.ac.uk/Record/cronfa22265
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first_indexed 2015-07-07T02:10:49Z
last_indexed 2018-02-09T05:00:34Z
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spelling 2015-07-06T08:46:52.4110338 v2 22265 2015-07-06 Around Ovsyannikov's method 4dc251ebcd7a89a15b71c846cd0ddaaf 0000-0001-7136-9399 Dmitri Finkelshtein Dmitri Finkelshtein true false 2015-07-06 SMA We study existence, uniqueness, and a limiting behaviour of solutions to an abstract linear evolution equation in a scale of Banach spaces. The generator of the equation is a perturbation of the operator which satisfies the classical assumptions of Ovsyannikov's method by a generator of a $C_0$-semigroup acting in each of the spaces of the scale. The results are (slightly modified) abstract version of those considered in [D. Finkelshtein, Y. Kondratiev, Y. Kozitsky, O.Kutoviy. The statistical dynamics of a spatial logistic model and the related kinetic equation. Math. Models Methods Appl. Sci., 25 (2): 343-370, 2015] for a particular equation. An application to a birth-and-death stochastic dynamics in the continuum is considered. Journal Article Methods of Functional Analysis and Topology 21 2 134 150 Ovsyannikov&apos;s method, scale of spaces, evolution equations, birth-and-death dynamics, Vlasov scaling, kinetic equation 31 12 2015 2015-12-31 http://www.imath.kiev.ua/~mfat/ COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2015-07-06T08:46:52.4110338 2015-07-06T08:46:52.4110338 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Dmitri Finkelshtein 0000-0001-7136-9399 1
title Around Ovsyannikov's method
spellingShingle Around Ovsyannikov's method
Dmitri Finkelshtein
title_short Around Ovsyannikov's method
title_full Around Ovsyannikov's method
title_fullStr Around Ovsyannikov's method
title_full_unstemmed Around Ovsyannikov's method
title_sort Around Ovsyannikov's method
author_id_str_mv 4dc251ebcd7a89a15b71c846cd0ddaaf
author_id_fullname_str_mv 4dc251ebcd7a89a15b71c846cd0ddaaf_***_Dmitri Finkelshtein
author Dmitri Finkelshtein
author2 Dmitri Finkelshtein
format Journal article
container_title Methods of Functional Analysis and Topology
container_volume 21
container_issue 2
container_start_page 134
publishDate 2015
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://www.imath.kiev.ua/~mfat/
document_store_str 0
active_str 0
description We study existence, uniqueness, and a limiting behaviour of solutions to an abstract linear evolution equation in a scale of Banach spaces. The generator of the equation is a perturbation of the operator which satisfies the classical assumptions of Ovsyannikov's method by a generator of a $C_0$-semigroup acting in each of the spaces of the scale. The results are (slightly modified) abstract version of those considered in [D. Finkelshtein, Y. Kondratiev, Y. Kozitsky, O.Kutoviy. The statistical dynamics of a spatial logistic model and the related kinetic equation. Math. Models Methods Appl. Sci., 25 (2): 343-370, 2015] for a particular equation. An application to a birth-and-death stochastic dynamics in the continuum is considered.
published_date 2015-12-31T03:26:30Z
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