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Frontières de domaines d’invariance et de viabilité pour des inclusions différentielles avec contraintes. (Boundaries of invariant and viability domains of differential inclusions with constraints). (French) Zbl 0705.34014

Summary: We explain where and how solutions of a differential inclusion can cross the boundary of a given closed set. In order to do this, we prove a new result on contingent cones of an intersection. Thanks to this, we show a property of the boundary of the viability kernel (i.e. the largest subset of initial conditions, from which there exist solutions staying in a given set of constraints). Qualitatively we describe the behaviour of these solutions in terms of viability and invariant domains of several sets. Finally, we give applications to target problems and differential games.

MSC:

34A60 Ordinary differential inclusions
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