2 research outputs found
A reinterpretation of set differential equations as differential equations in a Banach space
Set differential equations are usually formulated in terms of the Hukuhara
differential, which implies heavy restrictions for the nature of a solution. We
propose to reformulate set differential equations as ordinary differential
equations in a Banach space by identifying the convex and compact subsets of
with their support functions. Using this representation, we demonstrate
how existence and uniqueness results can be applied to set differential
equations. We provide a simple example, which can be treated in support
function representation, but not in the Hukuhara setting