Solving of Partial Differential Equations under Minimal Conditions
It is proved that a differentiable with respect to each variable function f : R2 → R is a solution of the equation ∂u/∂x + ∂u/∂y = 0 if and only if there exists a function φ : R → R such that f(x, y) = φ(x - y). This gives a positive answer to a question by R. Baire. Besides, this result is used to...
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| Опубліковано в: : | Журнал математической физики, анализа, геометрии |
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| Дата: | 2008 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2008
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/106505 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Solving of Partial Differential Equations under Minimal Conditions / V.K. Maslyuchenko, V.V. Mykhaylyuk // Журнал математической физики, анализа, геометрии. — 2008. — Т. 4, № 2. — С. 252-266. — Бібліогр.: 7 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862710929885495296 |
|---|---|
| author | Maslyuchenko, V.K. Mykhaylyuk, V.V. |
| author_facet | Maslyuchenko, V.K. Mykhaylyuk, V.V. |
| citation_txt | Solving of Partial Differential Equations under Minimal Conditions / V.K. Maslyuchenko, V.V. Mykhaylyuk // Журнал математической физики, анализа, геометрии. — 2008. — Т. 4, № 2. — С. 252-266. — Бібліогр.: 7 назв. — англ. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| description | It is proved that a differentiable with respect to each variable function f : R2 → R is a solution of the equation ∂u/∂x + ∂u/∂y = 0 if and only if there exists a function φ : R → R such that f(x, y) = φ(x - y). This gives a positive answer to a question by R. Baire. Besides, this result is used to solve analogous partial di erential equations in abstract spaces and partial differential equations of higher-order.
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| first_indexed | 2025-12-07T17:28:03Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106505 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T17:28:03Z |
| publishDate | 2008 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Maslyuchenko, V.K. Mykhaylyuk, V.V. 2016-09-29T18:06:34Z 2016-09-29T18:06:34Z 2008 Solving of Partial Differential Equations under Minimal Conditions / V.K. Maslyuchenko, V.V. Mykhaylyuk // Журнал математической физики, анализа, геометрии. — 2008. — Т. 4, № 2. — С. 252-266. — Бібліогр.: 7 назв. — англ. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106505 It is proved that a differentiable with respect to each variable function f : R2 → R is a solution of the equation ∂u/∂x + ∂u/∂y = 0 if and only if there exists a function φ : R → R such that f(x, y) = φ(x - y). This gives a positive answer to a question by R. Baire. Besides, this result is used to solve analogous partial di erential equations in abstract spaces and partial differential equations of higher-order. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии Solving of Partial Differential Equations under Minimal Conditions Article published earlier |
| spellingShingle | Solving of Partial Differential Equations under Minimal Conditions Maslyuchenko, V.K. Mykhaylyuk, V.V. |
| title | Solving of Partial Differential Equations under Minimal Conditions |
| title_full | Solving of Partial Differential Equations under Minimal Conditions |
| title_fullStr | Solving of Partial Differential Equations under Minimal Conditions |
| title_full_unstemmed | Solving of Partial Differential Equations under Minimal Conditions |
| title_short | Solving of Partial Differential Equations under Minimal Conditions |
| title_sort | solving of partial differential equations under minimal conditions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106505 |
| work_keys_str_mv | AT maslyuchenkovk solvingofpartialdifferentialequationsunderminimalconditions AT mykhaylyukvv solvingofpartialdifferentialequationsunderminimalconditions |