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.
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This research was supported by the National Sustainability Programme of the Czech Ministry of Education, Youth and Sports (LO1214) and the RECETOX research infrastructure (LM2015051 and CZ.02.1.01/0.0/0.0/16_013/0001761).
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Mazurenko, S.S. Viscosity solutions to evolution problems of star-shaped reachable sets. Nonlinear Differ. Equ. Appl. 25, 29 (2018). https://doi.org/10.1007/s00030-018-0516-8
Mathematics Subject Classification
- Differential inclusion
- Generalized solutions
- Radial function
- Minkowski function
- Gauge function