Notes on infinite-dimensional nonlinear parabolic equations
We present a method for the solution of the Cauchy problem for three broad classes of nonlinear parabolic equations $$\frac{{\partial U\left( {t,x} \right)}}{{\partial t}} = f\left( {\Delta _L U\left( {t,x} \right)} \right), \frac{{\partial U\left( {t,x} \right)}}{{\partial t}} f\left( {t,\Delta _...
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| Datum: | 2000 |
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| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2000
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4462 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510592379387904 |
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| author | Feller, M. N. Феллер, М. Н. Феллер, М. Н. |
| author_facet | Feller, M. N. Феллер, М. Н. Феллер, М. Н. |
| author_sort | Feller, M. N. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:29:27Z |
| description | We present a method for the solution of the Cauchy problem for three broad classes of nonlinear parabolic equations $$\frac{{\partial U\left( {t,x} \right)}}{{\partial t}} = f\left( {\Delta _L U\left( {t,x} \right)} \right), \frac{{\partial U\left( {t,x} \right)}}{{\partial t}} f\left( {t,\Delta _L U\left( {t,x} \right)} \right),$$ and $$\frac{{\partial U\left( {t,x} \right)}}{{\partial t}} = f\left( {U\left( {t,x} \right), \Delta _L U\left( {t,x} \right)} \right)$$ with the infinite-dimensional Laplacian ΔL. |
| first_indexed | 2026-03-24T02:59:27Z |
| format | Article |
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| id | umjimathkievua-article-4462 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:59:27Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/0b/ad0f4ce7a466442b1185eb9f21e9ab0b.pdf |
| spelling | umjimathkievua-article-44622020-03-18T20:29:27Z Notes on infinite-dimensional nonlinear parabolic equations Заметки о бесконечномерных нелинейных параболических уравнениях Feller, M. N. Феллер, М. Н. Феллер, М. Н. We present a method for the solution of the Cauchy problem for three broad classes of nonlinear parabolic equations $$\frac{{\partial U\left( {t,x} \right)}}{{\partial t}} = f\left( {\Delta _L U\left( {t,x} \right)} \right), \frac{{\partial U\left( {t,x} \right)}}{{\partial t}} f\left( {t,\Delta _L U\left( {t,x} \right)} \right),$$ and $$\frac{{\partial U\left( {t,x} \right)}}{{\partial t}} = f\left( {U\left( {t,x} \right), \Delta _L U\left( {t,x} \right)} \right)$$ with the infinite-dimensional Laplacian ΔL. Наведено метод розв'язання задачі Коші для трьох широких класів нелінійних параболічних рівнянь $$\frac{{\partial U\left( {t,x} \right)}}{{\partial t}} = f\left( {\Delta _L U\left( {t,x} \right)} \right), \frac{{\partial U\left( {t,x} \right)}}{{\partial t}} f\left( {t,\Delta _L U\left( {t,x} \right)} \right),$$ $$\frac{{\partial U\left( {t,x} \right)}}{{\partial t}} = f\left( {U\left( {t,x} \right), \Delta _L U\left( {t,x} \right)} \right)$$ із нескінченновимірним лапласіаном $Δ_L$. Institute of Mathematics, NAS of Ukraine 2000-05-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4462 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 5 (2000); 690-701 Український математичний журнал; Том 52 № 5 (2000); 690-701 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4462/5628 https://umj.imath.kiev.ua/index.php/umj/article/view/4462/5629 Copyright (c) 2000 Feller M. N. |
| spellingShingle | Feller, M. N. Феллер, М. Н. Феллер, М. Н. Notes on infinite-dimensional nonlinear parabolic equations |
| title | Notes on infinite-dimensional nonlinear parabolic equations |
| title_alt | Заметки о бесконечномерных нелинейных параболических уравнениях |
| title_full | Notes on infinite-dimensional nonlinear parabolic equations |
| title_fullStr | Notes on infinite-dimensional nonlinear parabolic equations |
| title_full_unstemmed | Notes on infinite-dimensional nonlinear parabolic equations |
| title_short | Notes on infinite-dimensional nonlinear parabolic equations |
| title_sort | notes on infinite-dimensional nonlinear parabolic equations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4462 |
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