Viscosity solutions to evolution problems of star-shaped reachable sets
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The article deals with Lipschitz continuous differential inclusions that yield star-shaped reachable sets. The purpose of the paper is to show that the radial function of such reachable sets is a viscosity solution to a certain partial differential equation. As a result, the existing theory of viscosity solutions to first-order partial differential equations was applied to resolve the existence, uniqueness, and some calculation aspects. Several relaxations concerning the forms of the inclusion and the initial set were also considered.
KeywordsDifferential inclusion Generalized solutions Radial function Minkowski function Gauge function
Mathematics Subject Classification35D40 93B03 34A60