Abstract
For a linear differential equation with the Hukuhara derivative and constant coefficient matrix, we obtain a necessary and sufficient condition under which every solution that is a polyhedron at the initial time remains a polyhedron (not necessarily with the same number of vertices) at all subsequent times.
Similar content being viewed by others
REFERENCES
Hukuhara, M., Intégration des applications measurables dont la valeur est un compact convexe, Funkc. Ekvacioj., 1967, vol. 10, pp. 205–223.
Lakshmikantham, V., Gnana, B.T., and Vasundhara, D.J., Theory of Set Differential Equations in Metric Spaces, London: Cambridge Sci. Publ., 2006.
Ocheretnyuk, E.V. and Slyn’ko, V.I., Qualitative analysis of solutions of nonlinear differential equations with the Hukuhara derivative in the space \(\mathrm {conv}\thinspace \mathbb {R}^{2}\), Differ. Equations, 2015, vol. 51, no. 8, pp. 998–1013.
Atamas’, I.V. and Slyn’ko, V.I., Liouville formula for some classes of differential equations with the Hukuhara derivative, Differ. Equations, 2019, vol. 55, no. 11, pp. 1407–1419.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by V. Potapchouck
Rights and permissions
About this article
Cite this article
Voidelevich, A.S. Time-Invariant Polyhedron-Preserving Linear Differential Equations with the Hukuhara Derivative. Diff Equat 56, 1664–1667 (2020). https://doi.org/10.1134/S00122661200120150
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S00122661200120150