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

Martin Rasmussen; Janosch Rieger; Kevin Webster

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arXiv · 1508.03206

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

Martin Rasmussen·Janosch Rieger·Kevin Webster

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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.

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BibTeX RIS

Martin Rasmussen, Janosch Rieger, Kevin Webster. 2015-08-13. A reinterpretation of set differential equations as differential equations in a Banach space. https://arxiv.org/abs/1508.03206

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