Viability property on Riemannian manifolds
Shigē Péng, Xuehong Zhu · Comptes Rendus Mathématique · 2009
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 .