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...
Gespeichert in:
| Veröffentlicht in: | Журнал математической физики, анализа, геометрии |
|---|---|
| Datum: | 2008 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2008
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/106505 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-106505 |
|---|---|
| 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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Solving of Partial Differential Equations under Minimal Conditions |
| spellingShingle |
Solving of Partial Differential Equations under Minimal Conditions Maslyuchenko, V.K. Mykhaylyuk, V.V. |
| 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 |
| author |
Maslyuchenko, V.K. Mykhaylyuk, V.V. |
| author_facet |
Maslyuchenko, V.K. Mykhaylyuk, V.V. |
| publishDate |
2008 |
| language |
English |
| container_title |
Журнал математической физики, анализа, геометрии |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| format |
Article |
| 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.
|
| issn |
1812-9471 |
| url |
https://nasplib.isofts.kiev.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. |
| work_keys_str_mv |
AT maslyuchenkovk solvingofpartialdifferentialequationsunderminimalconditions AT mykhaylyukvv solvingofpartialdifferentialequationsunderminimalconditions |
| first_indexed |
2025-12-07T17:28:03Z |
| last_indexed |
2025-12-07T17:28:03Z |
| _version_ |
1850871365096177664 |