Viscosity solutions to evolution problems of star-shaped reachable sets
| Authors | |
|---|---|
| Year of publication | 2018 |
| Type | Article in Periodical |
| Magazine / Source | NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS |
| MU Faculty or unit | |
| 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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