Criteria for the Well-Posedness of the Cauchy Problem for Differential Operator Equations of Arbitrary Order
In Banach spaces, we investigate the differential equation \(\mathop \sum \nolimits_{j = 0}^n \;A_j u^{(j)} (t) = 0\) with closed linear operators A j (generally speaking, the operator coefficient A n of the higher derivative is degenerate). We obtain well-posedness conditions that character...
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| Datum: | 2004 |
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Institute of Mathematics, NAS of Ukraine
2004
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| author | Vlasenko, L. A. Piven’, A. L. Rutkas, A. G. Власенко, Л. А. Пивень, А. Л. Руткас, А. Г. Власенко, Л. А. Пивень, А. Л. Руткас, А. Г. |
| author_facet | Vlasenko, L. A. Piven’, A. L. Rutkas, A. G. Власенко, Л. А. Пивень, А. Л. Руткас, А. Г. Власенко, Л. А. Пивень, А. Л. Руткас, А. Г. |
| author_sort | Vlasenko, L. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:12:48Z |
| description | In Banach spaces, we investigate the differential equation \(\mathop \sum \nolimits_{j = 0}^n \;A_j u^{(j)} (t) = 0\) with closed linear operators A j (generally speaking, the operator coefficient A n of the higher derivative is degenerate). We obtain well-posedness conditions that characterize the continuous dependence of solutions and their derivatives on initial data. Abstract results are applied to partial differential equations. |
| first_indexed | 2026-03-24T02:49:58Z |
| format | Article |
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| id | umjimathkievua-article-3860 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
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| language | rus English |
| last_indexed | 2026-03-24T02:49:58Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/db/3afd62872316d7448ac06e0d33f77fdb.pdf |
| spelling | umjimathkievua-article-38602020-03-18T20:12:48Z Criteria for the Well-Posedness of the Cauchy Problem for Differential Operator Equations of Arbitrary Order Признаки корректности задачи Коши для дифференциально-операторных уравнений произвольного порядка Vlasenko, L. A. Piven’, A. L. Rutkas, A. G. Власенко, Л. А. Пивень, А. Л. Руткас, А. Г. Власенко, Л. А. Пивень, А. Л. Руткас, А. Г. In Banach spaces, we investigate the differential equation \(\mathop \sum \nolimits_{j = 0}^n \;A_j u^{(j)} (t) = 0\) with closed linear operators A j (generally speaking, the operator coefficient A n of the higher derivative is degenerate). We obtain well-posedness conditions that characterize the continuous dependence of solutions and their derivatives on initial data. Abstract results are applied to partial differential equations. У банаховнх просторах досліджується диференціальне рівняння $\mathop \sum \nolimits_{j = 0}^n \;A_j u^{(j)} (t) = 0$ замкненими лінійними операторами $A_j$ (взагалі кажучи, оператор $A_n$ при старшій похідній є виродженим). Одержано умови коректності, що характеризують неперервну залежність розв'язків та їх похідних від початкових даних. Абстрактні результати застосовуються до рівнянь з частинними похідними. Institute of Mathematics, NAS of Ukraine 2004-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3860 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 11 (2004); 1484-1500 Український математичний журнал; Том 56 № 11 (2004); 1484-1500 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/3860/4439 https://umj.imath.kiev.ua/index.php/umj/article/view/3860/4440 Copyright (c) 2004 Vlasenko L. A.; Piven’ A. L.; Rutkas A. G. |
| spellingShingle | Vlasenko, L. A. Piven’, A. L. Rutkas, A. G. Власенко, Л. А. Пивень, А. Л. Руткас, А. Г. Власенко, Л. А. Пивень, А. Л. Руткас, А. Г. Criteria for the Well-Posedness of the Cauchy Problem for Differential Operator Equations of Arbitrary Order |
| title | Criteria for the Well-Posedness of the Cauchy Problem for Differential Operator Equations of Arbitrary Order |
| title_alt | Признаки корректности задачи Коши
для дифференциально-операторных уравнений произвольного порядка |
| title_full | Criteria for the Well-Posedness of the Cauchy Problem for Differential Operator Equations of Arbitrary Order |
| title_fullStr | Criteria for the Well-Posedness of the Cauchy Problem for Differential Operator Equations of Arbitrary Order |
| title_full_unstemmed | Criteria for the Well-Posedness of the Cauchy Problem for Differential Operator Equations of Arbitrary Order |
| title_short | Criteria for the Well-Posedness of the Cauchy Problem for Differential Operator Equations of Arbitrary Order |
| title_sort | criteria for the well-posedness of the cauchy problem for differential operator equations of arbitrary order |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3860 |
| work_keys_str_mv | AT vlasenkola criteriaforthewellposednessofthecauchyproblemfordifferentialoperatorequationsofarbitraryorder AT pivenal criteriaforthewellposednessofthecauchyproblemfordifferentialoperatorequationsofarbitraryorder AT rutkasag criteriaforthewellposednessofthecauchyproblemfordifferentialoperatorequationsofarbitraryorder AT vlasenkola criteriaforthewellposednessofthecauchyproblemfordifferentialoperatorequationsofarbitraryorder AT pivenʹal criteriaforthewellposednessofthecauchyproblemfordifferentialoperatorequationsofarbitraryorder AT rutkasag criteriaforthewellposednessofthecauchyproblemfordifferentialoperatorequationsofarbitraryorder AT vlasenkola criteriaforthewellposednessofthecauchyproblemfordifferentialoperatorequationsofarbitraryorder AT pivenʹal criteriaforthewellposednessofthecauchyproblemfordifferentialoperatorequationsofarbitraryorder AT rutkasag criteriaforthewellposednessofthecauchyproblemfordifferentialoperatorequationsofarbitraryorder AT vlasenkola priznakikorrektnostizadačikošidlâdifferencialʹnooperatornyhuravnenijproizvolʹnogoporâdka AT pivenal priznakikorrektnostizadačikošidlâdifferencialʹnooperatornyhuravnenijproizvolʹnogoporâdka AT rutkasag priznakikorrektnostizadačikošidlâdifferencialʹnooperatornyhuravnenijproizvolʹnogoporâdka AT vlasenkola priznakikorrektnostizadačikošidlâdifferencialʹnooperatornyhuravnenijproizvolʹnogoporâdka AT pivenʹal priznakikorrektnostizadačikošidlâdifferencialʹnooperatornyhuravnenijproizvolʹnogoporâdka AT rutkasag priznakikorrektnostizadačikošidlâdifferencialʹnooperatornyhuravnenijproizvolʹnogoporâdka AT vlasenkola priznakikorrektnostizadačikošidlâdifferencialʹnooperatornyhuravnenijproizvolʹnogoporâdka AT pivenʹal priznakikorrektnostizadačikošidlâdifferencialʹnooperatornyhuravnenijproizvolʹnogoporâdka AT rutkasag priznakikorrektnostizadačikošidlâdifferencialʹnooperatornyhuravnenijproizvolʹnogoporâdka |