Geodesic
A variational approach to implicit ODEs and differential inclusions
ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 139-148

Voir la notice de l'article provenant de la source Numdam

An alternative approach for the analysis and the numerical approximation of ODEs, using a variational framework, is presented. It is based on the natural and elementary idea of minimizing the residual of the differential equation measured in a usual L p norm. Typical existence results for Cauchy problems can thus be recovered, and finer sets of assumptions for existence are made explicit. We treat, in particular, the cases of an explicit ODE and a differential inclusion. This approach also allows for a whole strategy to approximate numerically the solution. It is briefly indicated here as it will be pursued systematically and in a much more broad fashion in a subsequent paper.

DOI : 10.1051/cocv:2008020
Classification : 34A12, 49J05, 65L05
Keywords: variational methods, convexity, coercivity, value function 
@article{COCV_2009__15_1_139_0,
     author = {Amat, Sergio and Pedregal, Pablo},
     title = {A variational approach to implicit {ODEs} and differential inclusions},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {139--148},
     publisher = {EDP-Sciences},
     volume = {15},
     number = {1},
     year = {2009},
     doi = {10.1051/cocv:2008020},
     mrnumber = {2488572},
     zbl = {1172.34002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008020/}
}
TY  - JOUR
AU  - Amat, Sergio
AU  - Pedregal, Pablo
TI  - A variational approach to implicit ODEs and differential inclusions
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2009
SP  - 139
EP  - 148
VL  - 15
IS  - 1
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008020/
DO  - 10.1051/cocv:2008020
LA  - en
ID  - COCV_2009__15_1_139_0
ER  - 
%0 Journal Article
%A Amat, Sergio
%A Pedregal, Pablo
%T A variational approach to implicit ODEs and differential inclusions
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2009
%P 139-148
%V 15
%N 1
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008020/
%R 10.1051/cocv:2008020
%G en
%F COCV_2009__15_1_139_0
Amat, Sergio; Pedregal, Pablo. A variational approach to implicit ODEs and differential inclusions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 139-148. doi: 10.1051/cocv:2008020

Cité par Sources :