Viscosity solutions to evolution problems of star-shaped reachable sets

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Authors

MAZURENKO Stanislav

Year of publication 2018
Type Article in Periodical
Magazine / Source NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
MU Faculty or unit

Faculty of Science

Citation
Web https://link.springer.com/article/10.1007%2Fs00030-018-0516-8
Doi http://dx.doi.org/10.1007/s00030-018-0516-8
Keywords Differential inclusion; Generalized solutions; Radial function; Minkowski function; Gauge function
Description 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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