Viability of boundary of the viability kernel
Viability kernel for the following system \(x'(t)\in F(x(t))\), x(t)\(\in K\) is the largest viable subset of the set K. In the paper, some known properties of viability kernels are stated. Moreover, it is proved that for \(x_ 0\in int(K)\) in the boundary of the viability kernel there exists a solution starting from \(x_ 0\) that stays in the boundary of the viability kernel for some positive time, i.e., the boundary of the viability kernel is locally viable. If the viability kernel is a subset of int(K) then its boundary is (globally) viable.
scientific article; zbMATH DE number 4210565