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Viscosity solutions to evolution problems of star-shaped reachable sets

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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.

Keywords

Differential inclusion Generalized solutions Radial function Minkowski function Gauge function 

Mathematics Subject Classification

35D40 93B03 34A60 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Science, Research Centre for Toxic Compounds in the Environment RECETOX, Loschmidt LaboratoriesMasaryk UniversityBrnoCzech Republic

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