On the existence of global attractors for one class of cascade systems
We investigate the qualitative behavior of solutions of cascade systems without uniqueness. We prove that solutions of a reaction-diffusion system perturbed by a system of ordinary differential equations and solutions of a system of equations of a viscous incompressible liquid with passive component...
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| Date: | 2004 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2004
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3842 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509977025708032 |
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| author | Kapustyan, O. V. Капустян, О. В. |
| author_facet | Kapustyan, O. V. Капустян, О. В. |
| author_sort | Kapustyan, O. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:12:11Z |
| description | We investigate the qualitative behavior of solutions of cascade systems without uniqueness. We prove that solutions of a reaction-diffusion system perturbed by a system of ordinary differential equations and solutions of a system of equations of a viscous incompressible liquid with passive components form families of many-valued semiprocesses for which a compact global attractor exists in the phase space. |
| first_indexed | 2026-03-24T02:49:40Z |
| format | Article |
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| id | umjimathkievua-article-3842 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:49:40Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/8f/7e63c18d0b134ed5d86d0b4d38537c8f.pdf |
| spelling | umjimathkievua-article-38422020-03-18T20:12:11Z On the existence of global attractors for one class of cascade systems Про існування глобальних атракторі» для одного класу каскадних систем Kapustyan, O. V. Капустян, О. В. We investigate the qualitative behavior of solutions of cascade systems without uniqueness. We prove that solutions of a reaction-diffusion system perturbed by a system of ordinary differential equations and solutions of a system of equations of a viscous incompressible liquid with passive components form families of many-valued semiprocesses for which a compact global attractor exists in the phase space. Досліджується якісна поведінка розв'язків каскадних систем без єдииості. Доведено, що розв'язки системи реакції-дифузії, збуреної системою звичайних диференціальних рівнянь, і розв'язки системи рівнянь в'язкої нестисливої рідини з пасивними складовими утворюють сім'ї багатозначних напівпроцесів, для яких у фазовому просторі існує компактний глобальний атрактор. Institute of Mathematics, NAS of Ukraine 2004-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3842 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 9 (2004); 1287-1291 Український математичний журнал; Том 56 № 9 (2004); 1287-1291 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/3842/4403 https://umj.imath.kiev.ua/index.php/umj/article/view/3842/4404 Copyright (c) 2004 Kapustyan O. V. |
| spellingShingle | Kapustyan, O. V. Капустян, О. В. On the existence of global attractors for one class of cascade systems |
| title | On the existence of global attractors for one class of cascade systems |
| title_alt | Про існування глобальних атракторі» для одного класу каскадних
систем |
| title_full | On the existence of global attractors for one class of cascade systems |
| title_fullStr | On the existence of global attractors for one class of cascade systems |
| title_full_unstemmed | On the existence of global attractors for one class of cascade systems |
| title_short | On the existence of global attractors for one class of cascade systems |
| title_sort | on the existence of global attractors for one class of cascade systems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3842 |
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