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@article{Rasmussen:2018:10.1017/S0308210517000178,
author = {Rasmussen, M and Rieger, J and Webster, KN},
doi = {10.1017/S0308210517000178},
journal = {Proceedings of the Royal Society of Edinburgh Section A-Mathematics},
pages = {429--446},
title = {A reinterpretation of set differential equations as differential equations in a Banach space},
url = {http://dx.doi.org/10.1017/S0308210517000178},
volume = {148},
year = {2018}
}

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TY  - JOUR
AB  - Set  differential  equations  are  usually  formulated  in  terms  of  theHukuhara differential.  As a consequence, the theory of set differentialequations is perceived as an independent subject, in which all resultsare proved within the framework of the Hukuhara calculus.We  propose  to  reformulate  set  differential  equations  as  ordinarydifferential equations in a Banach space by identifying the convex andcompact subsets ofRdwith their support functions.  Using this rep-resentation, standard existence and uniqueness theorems for ordinarydifferential equations can be applied to set differential equations.  Weprovide a geometric interpretation of the main result, and we demon-strate that our approach overcomes the heavy restrictions the use ofthe Hukuhara differential implies for the nature of a solution.
AU  - Rasmussen,M
AU  - Rieger,J
AU  - Webster,KN
DO  - 10.1017/S0308210517000178
EP  - 446
PY  - 2018///
SN  - 1473-7124
SP  - 429
TI  - A reinterpretation of set differential equations as differential equations in a Banach space
T2  - Proceedings of the Royal Society of Edinburgh Section A-Mathematics
UR  - http://dx.doi.org/10.1017/S0308210517000178
UR  - http://hdl.handle.net/10044/1/48071
VL  - 148
ER  -

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