Boundary-value problems for stationary Hamilton-Jacobi and Bellman equations
We introduce solutions of boundary-value problems for the stationary Hamilton-Jacobi and Bellman equations in functional spaces (semimodules) with a special algebraic structure adapted to these problems. In these spaces, we obtain representations of solutions in terms of “basic” ones and prove a the...
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| Date: | 1997 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1997
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5016 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511212162252800 |
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| author | Maslov, V. P. Samborsky, S. N. Маслов, В. П. Самборский, С. Н. Маслов, В. П. Самборский, С. Н. |
| author_facet | Maslov, V. P. Samborsky, S. N. Маслов, В. П. Самборский, С. Н. Маслов, В. П. Самборский, С. Н. |
| author_sort | Maslov, V. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:22:53Z |
| description | We introduce solutions of boundary-value problems for the stationary Hamilton-Jacobi and Bellman equations in functional spaces (semimodules) with a special algebraic structure adapted to these problems. In these spaces, we obtain representations of solutions in terms of “basic” ones and prove a theorem on approximation of these solutions in the case where nonsmooth Hamiltonians are approximated by smooth Hamiltonians. This approach is an alternative to the maximum principle. |
| first_indexed | 2026-03-24T03:09:18Z |
| format | Article |
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| id | umjimathkievua-article-5016 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:09:18Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/d5/3cd9225aa71b8bdeab4e1a104d4f3ed5.pdf |
| spelling | umjimathkievua-article-50162020-03-18T21:22:53Z Boundary-value problems for stationary Hamilton-Jacobi and Bellman equations Краевые задачи для стационарных уравнений Гамильтона—Якоби и Беллмана Maslov, V. P. Samborsky, S. N. Маслов, В. П. Самборский, С. Н. Маслов, В. П. Самборский, С. Н. We introduce solutions of boundary-value problems for the stationary Hamilton-Jacobi and Bellman equations in functional spaces (semimodules) with a special algebraic structure adapted to these problems. In these spaces, we obtain representations of solutions in terms of “basic” ones and prove a theorem on approximation of these solutions in the case where nonsmooth Hamiltonians are approximated by smooth Hamiltonians. This approach is an alternative to the maximum principle. Внодяться розв'язки граничних задач для стаціонарних рівнянь Гамільтона-Якобі та Беллмапа и функціональних просторах (семімодулях) зі спеціальною алгебраїчною структурою, яка відповідає цим задачам. В означених просторах одержані представлення розв'язків через „базисні", а також теорема про їх апроксимацію при апроксимації негладких гамільтоніанів гладкими. Підхід являє собою альтернативу принципу максимума. Institute of Mathematics, NAS of Ukraine 1997-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5016 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 3 (1997); 433–447 Український математичний журнал; Том 49 № 3 (1997); 433–447 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5016/6731 https://umj.imath.kiev.ua/index.php/umj/article/view/5016/6732 Copyright (c) 1997 Maslov V. P.; Samborsky S. N. |
| spellingShingle | Maslov, V. P. Samborsky, S. N. Маслов, В. П. Самборский, С. Н. Маслов, В. П. Самборский, С. Н. Boundary-value problems for stationary Hamilton-Jacobi and Bellman equations |
| title | Boundary-value problems for stationary Hamilton-Jacobi and Bellman equations |
| title_alt | Краевые задачи для стационарных уравнений
Гамильтона—Якоби и Беллмана |
| title_full | Boundary-value problems for stationary Hamilton-Jacobi and Bellman equations |
| title_fullStr | Boundary-value problems for stationary Hamilton-Jacobi and Bellman equations |
| title_full_unstemmed | Boundary-value problems for stationary Hamilton-Jacobi and Bellman equations |
| title_short | Boundary-value problems for stationary Hamilton-Jacobi and Bellman equations |
| title_sort | boundary-value problems for stationary hamilton-jacobi and bellman equations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5016 |
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