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Mazurenko, S. S.

Viscosity solutions to evolution problems of star-shaped reachable sets. (English) Zbl 1403.34017

NoDEA, Nonlinear Differ. Equ. Appl. 25, No. 4, Paper No. 29, 23 p. (2018).
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.
Reviewer: Patrick Winkert (Berlin)

MSC:

34A60 Ordinary differential inclusions
35D40 Viscosity solutions to PDEs
93B03 Attainable sets, reachability

Keywords:

differential inclusion; generalized solutions; radial function; Minkowski function; gauge function
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\textit{S. S. Mazurenko}, NoDEA, Nonlinear Differ. Equ. Appl. 25, No. 4, Paper No. 29, 23 p. (2018; Zbl 1403.34017)
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