Geodesic
Applications of the Carathéodory theorem to PDEs
Annales Polonici Mathematici, Tome 73 (2000) no. 1, pp. 1-27.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ap-73-1-1-27
Mots-clés : Carathéodory theorem, product integral, Galerkin method

Konstanty Holly 1 ; Joanna Orewczyk 1

1 
@article{10_4064_ap_73_1_1_27,
     author = {Konstanty Holly and Joanna Orewczyk},
     title = {Applications of the {Carath\'eodory} theorem to {PDEs}},
     journal = {Annales Polonici Mathematici},
     pages = {1--27},
     publisher = {mathdoc},
     volume = {73},
     number = {1},
     year = {2000},
     doi = {10.4064/ap-73-1-1-27},
     language = {fr},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-73-1-1-27/}
}
TY  - JOUR
AU  - Konstanty Holly
AU  - Joanna Orewczyk
TI  - Applications of the Carathéodory theorem to PDEs
JO  - Annales Polonici Mathematici
PY  - 2000
SP  - 1
EP  - 27
VL  - 73
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap-73-1-1-27/
DO  - 10.4064/ap-73-1-1-27
LA  - fr
ID  - 10_4064_ap_73_1_1_27
ER  - 
%0 Journal Article
%A Konstanty Holly
%A Joanna Orewczyk
%T Applications of the Carathéodory theorem to PDEs
%J Annales Polonici Mathematici
%D 2000
%P 1-27
%V 73
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ap-73-1-1-27/
%R 10.4064/ap-73-1-1-27
%G fr
%F 10_4064_ap_73_1_1_27
Konstanty Holly; Joanna Orewczyk. Applications of the Carathéodory theorem to PDEs. Annales Polonici Mathematici, Tome 73 (2000) no. 1, pp. 1-27. doi : 10.4064/ap-73-1-1-27. http://geodesic.mathdoc.fr/articles/10.4064/ap-73-1-1-27/

Cité par Sources :