On the Stabilization of a Solution of the Cauchy Problem for One Class of Integro-Differential Equations
We consider a solution of the Cauchy problem u(t, x), t > 0, x ∈ R 2, for one class of integro-differential equations. These equations have the following specific feature: the matrix of the coefficients of higher derivatives is degenerate for all x. We establish conditions for the existence o...
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| Date: | 2004 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2004
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3877 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510008751423488 |
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| author | Kulinich, G. L. Kushnirenko, S. V. Кулініч, Г. Л. Кушніренко, С. В. |
| author_facet | Kulinich, G. L. Kushnirenko, S. V. Кулініч, Г. Л. Кушніренко, С. В. |
| author_sort | Kulinich, G. L. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:13:06Z |
| description | We consider a solution of the Cauchy problem u(t, x), t > 0, x ∈ R 2, for one class of integro-differential equations. These equations have the following specific feature: the matrix of the coefficients of higher derivatives is degenerate for all x. We establish conditions for the existence of the limit lim t→∞ u(t, x) = v(x) and represent the solution of the Cauchy problem in explicit form in terms of the coefficients of the equation. |
| first_indexed | 2026-03-24T02:50:10Z |
| format | Article |
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| id | umjimathkievua-article-3877 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:50:10Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/9e/2694e7c6494b29aeb13d0645072f349e.pdf |
| spelling | umjimathkievua-article-38772020-03-18T20:13:06Z On the Stabilization of a Solution of the Cauchy Problem for One Class of Integro-Differential Equations Про стабілізацію розв'язку задачі Коші для певного класу інтегро-диференціальних рівнянь Kulinich, G. L. Kushnirenko, S. V. Кулініч, Г. Л. Кушніренко, С. В. We consider a solution of the Cauchy problem u(t, x), t > 0, x ∈ R 2, for one class of integro-differential equations. These equations have the following specific feature: the matrix of the coefficients of higher derivatives is degenerate for all x. We establish conditions for the existence of the limit lim t→∞ u(t, x) = v(x) and represent the solution of the Cauchy problem in explicit form in terms of the coefficients of the equation. Розглядається розв'язок задачі Коші $u(t, x), t > 0, x ∈ R^2$, певного класу інгегро-диференціальних рівнянь. Характерною особливістю цих рівнянь є те, що матриця із коефіцієїггів при старших похідних є виродженою при всіх $x$. Отримано умови, при яких існує границя $\lim_{t→∞} u(t, x) = v(x)$. При цьому наведено явний вигляд розв'язку задачі Коші, який виражаться безпосередньо через коефіцієнти рівняння. Institute of Mathematics, NAS of Ukraine 2004-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3877 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 12 (2004); 1699 – 1706 Український математичний журнал; Том 56 № 12 (2004); 1699 – 1706 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/3877/4471 https://umj.imath.kiev.ua/index.php/umj/article/view/3877/4472 Copyright (c) 2004 Kulinich G. L.; Kushnirenko S. V. |
| spellingShingle | Kulinich, G. L. Kushnirenko, S. V. Кулініч, Г. Л. Кушніренко, С. В. On the Stabilization of a Solution of the Cauchy Problem for One Class of Integro-Differential Equations |
| title | On the Stabilization of a Solution of the Cauchy Problem for One Class of Integro-Differential Equations |
| title_alt | Про стабілізацію розв'язку задачі Коші для певного
класу інтегро-диференціальних рівнянь |
| title_full | On the Stabilization of a Solution of the Cauchy Problem for One Class of Integro-Differential Equations |
| title_fullStr | On the Stabilization of a Solution of the Cauchy Problem for One Class of Integro-Differential Equations |
| title_full_unstemmed | On the Stabilization of a Solution of the Cauchy Problem for One Class of Integro-Differential Equations |
| title_short | On the Stabilization of a Solution of the Cauchy Problem for One Class of Integro-Differential Equations |
| title_sort | on the stabilization of a solution of the cauchy problem for one class of integro-differential equations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3877 |
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