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Comptes Rendus Mathématique
Volume 347, n° 23-24
pages 1423-1428 (décembre 2009)
Doi : 10.1016/j.crma.2009.10.007
Received : 16 October 2008 ;  accepted : 2 October 2009
Viability property on Riemannian manifolds
Propriété de viabilité sur une variété riemannienne
 

Shige Peng a , Xuehong Zhu a, b
a Institute of Mathematics, Shandong University, Jinan, 250100, China 
b School of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China 

Abstract

This Note studies a sufficient and necessary condition for the viability property of a state system in a closed subset K of a finite-dimensional compact Riemannian manifold without boundary. Our result is: the system enjoys the viability property in K if and only if the square of the distance function of K is a viscosity supersolution of a second-order partial differential equation in some neighborhood of K . To cite this article: S. Peng, X. Zhu, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

The full text of this article is available in PDF format.
Résumé

Dans cette Note on donne une condition nécessaire et suffisante pour que soit satisfaite la propriété de viabilité d’un système sur un sous-ensemble K d’une variété riemannienne, de dimension finie, sans bord. Le résultat s’énonce ainsi : le système sur K possède la propriété de viabilité si et seulement si le carré de la fonction distance à K est une sursolution de viscosité d’une équation aux dérivées partielles du second ordre définie sur un voisinage de K . Pour citer cet article : S. Peng, X. Zhu, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

The full text of this article is available in PDF format.


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