A variational approach to implicit ODEs and differential inclusions
2009 - S. Amat, P. Pedregal
ESAIM: Control, Optimisation and Calculus of Variations 15, 139-148 (2009)
authors IMACI
Abtract
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 Lpnorm. 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.