Viscosity solutions to evolution problems of star-shaped reachable sets

Investor logo
Investor logo

Warning

This publication doesn't include Faculty of Economics and Administration. It includes Faculty of Science. Official publication website can be found on muni.cz.
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.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.