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@article{1503896,
author = {Mazurenko, Stanislav},
article_location = {BASEL},
article_number = {4},
doi = {http://dx.doi.org/10.1007/s00030-018-0516-8},
keywords = {Differential inclusion; Generalized solutions; Radial function; Minkowski function; Gauge function},
language = {eng},
issn = {1021-9722},
journal = {NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS},
title = {Viscosity solutions to evolution problems of star-shaped reachable sets},
url = {https://link.springer.com/article/10.1007%2Fs00030-018-0516-8},
volume = {25},
year = {2018}
}
TY - JOUR
ID - 1503896
AU - Mazurenko, Stanislav
PY - 2018
TI - Viscosity solutions to evolution problems of star-shaped reachable sets
JF - NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
VL - 25
IS - 4
SP - 1-23
EP - 1-23
PB - SPRINGER BASEL AG
SN - 10219722
KW - Differential inclusion
KW - Generalized solutions
KW - Radial function
KW - Minkowski function
KW - Gauge function
UR - https://link.springer.com/article/10.1007%2Fs00030-018-0516-8
L2 - https://link.springer.com/article/10.1007%2Fs00030-018-0516-8
N2 - 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.
ER -
MAZURENKO, Stanislav. Viscosity solutions to evolution problems of star-shaped reachable sets. \textit{NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS}. BASEL: SPRINGER BASEL AG, 2018, roč.~25, č.~4, s.~1-23. ISSN~1021-9722. Dostupné z: https://dx.doi.org/10.1007/s00030-018-0516-8.
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