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:
| Datum: | 2008 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2008
|
| Schriftenreihe: | Журнал математической физики, анализа, геометрии |
| Online Zugang: | http://dspace.nbuv.gov.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| Zusammenfassung: | 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. |
|---|