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Viscosity solutions to evolution problems of star-shaped reachable sets. (English) Zbl 1403.34017
Author’s abstract: 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.
MSC:
34A60 Ordinary differential inclusions
35D40 Viscosity solutions to PDEs
93B03 Attainable sets, reachability
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