A reinterpretation of set differential equations as differential equations in a Banach space

Abstract

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 $\R^d$ 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.