- Tytuł:
- Applications of the Carathéodory theorem to PDEs
- Autorzy:
-
Holly, Konstanty
Orewczyk, Joanna - Powiązania:
- https://bibliotekanauki.pl/articles/1208027.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Carathéodory theorem
product integral
Galerkin method - Opis:
- We discuss and exploit the Carathéodory theorem on existence and uniqueness of an absolutely continuous solution x: ℐ (⊂ ℝ) → X of a general ODE $ẋ {(*)\over=} ℱ(t,x)$ for the right-hand side ℱ : dom ℱ ( ⊂ ℝ × X) → X taking values in an arbitrary Banach space X, and a related result concerning an extension of x. We propose a definition of solvability of (*) admitting all connected ℐ and unifying the cases "dom ℱ is open" and "dom ℱ = ℐ × Ω for some Ω ⊂ X". We show how to use the theorems mentioned above to get approximate solutions of a nonlinear parabolic PDE and exact solutions of a linear evolution PDE with distribution data.
- Źródło:
-
Annales Polonici Mathematici; 2000, 73, 1; 1-27
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki