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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| Дата: | 2008 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2008
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
irk-123456789-106505 |
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dspace |
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irk-123456789-1065052016-09-30T03:02:53Z Solving of Partial Differential Equations under Minimal Conditions Maslyuchenko, V.K. Mykhaylyuk, V.V. 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. 2008 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/106505 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Maslyuchenko, V.K. Mykhaylyuk, V.V. |
| spellingShingle |
Maslyuchenko, V.K. Mykhaylyuk, V.V. Solving of Partial Differential Equations under Minimal Conditions Журнал математической физики, анализа, геометрии |
| author_facet |
Maslyuchenko, V.K. Mykhaylyuk, V.V. |
| author_sort |
Maslyuchenko, V.K. |
| title |
Solving of Partial Differential Equations under Minimal Conditions |
| title_short |
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_sort |
solving of partial differential equations under minimal conditions |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106505 |
| 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. |
| series |
Журнал математической физики, анализа, геометрии |
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AT maslyuchenkovk solvingofpartialdifferentialequationsunderminimalconditions AT mykhaylyukvv solvingofpartialdifferentialequationsunderminimalconditions |
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2023-10-18T20:13:06Z |
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2023-10-18T20:13:06Z |
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1796149283075915776 |