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Set-valued solutions to the Cauchy problem for hyperbolic systems of partial differential inclusions

Aubin, Jean-Pierre; Frankowska, Halina (1997), Set-valued solutions to the Cauchy problem for hyperbolic systems of partial differential inclusions, NoDEA: Nonlinear Differential Equations and Applications, 4, 2, p. 149-168. http://dx.doi.org/10.1007/PL00001413

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Type
Article accepté pour publication ou publié
Date
1997
Journal name
NoDEA: Nonlinear Differential Equations and Applications
Volume
4
Number
2
Publisher
Springer
Pages
149-168
Publication identifier
http://dx.doi.org/10.1007/PL00001413
Metadata
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Author(s)
Aubin, Jean-Pierre
Frankowska, Halina
Abstract (FR)
On démontre l'existence de solutions multivoques globales du problème de Cauchy pour les systèmes hyperboliques du premier ordre d'équations ou d'inclusions aux dérivées partielles, pour des conditions initiales univoques ou multivoques. La méthode est basée sur l'équivalence entre ce problème et celui de l'existence de tubes de viabilité pour le système caractéristique d'équations différentielles ordinaires ou d'inclusions différentielles.
Abstract (EN)
We prove the existence of global set-valued solutions to the Cauchy problem for partial differential equations and inclusions, with either single-valued or set-valued initial conditions. The method is based on the equivalence between this problem and problem of finding viability tubes of the associated characteristic system of ordinary differential equations. As an application we construct the value function of the Mayer problem arising in control theory.
Subjects / Keywords
inclusions; partial differential equations; Cauchy problem

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