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A variational approach to implicit ODEs and differential inclusions

Published online by Cambridge University Press:  23 January 2009

Sergio Amat  and
Pablo Pedregal
Sergio Amat
Affiliation:
Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain. [email protected]
Pablo Pedregal
Affiliation:
E.T.S. Ingenieros Industriales, Universidad de Castilla La Mancha, Campus de Ciudad Real, Spain. [email protected]
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Abstract

An alternative approach for the analysis and the numericalapproximation of ODEs, using a variational framework, ispresented. It is based on the natural and elementary idea of minimizing the residual of the differential equation measured in a usual Lp norm.Typical existence results for Cauchy problems can thus berecovered, 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.

Keywords

Variational methodsconvexitycoercivityvalue function
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 1 , January 2009 , pp. 139 - 148
Copyright
© EDP Sciences, SMAI, 2008

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References

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