Optimal transport in competition with reaction: The Hellinger-Kantorovich distance and geodesic curves
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2160 | |
dc.contributor.author | Liero, Matthias | |
dc.contributor.author | Mielke, Alexander | |
dc.contributor.author | Savaré, Giuseppe | |
dc.date.accessioned | 2016-12-13T10:46:48Z | |
dc.date.available | 2019-06-28T08:25:39Z | |
dc.date.issued | 2015 | |
dc.description.abstract | We discuss a new notion of distance on the space of finite and nonnegative measures on Omega C Rd, which we call Hellinger-Kantorovich distance. It can be seen as an infconvolution of the well-known Kantorovich-Wasserstein distance and the Hellinger-Kakutani distance. The new distance is based on a dynamical formulation given by an Onsager operator that is the sum of a Wasserstein diffusion part and an additional reaction part describing the generation and absorption of mass. We present a full characterization of the distance and some of its properties. In particular, the distance can be equivalently described by an optimal transport problem on the cone space over the underlying space Omega. We give a construction of geodesic curves and discuss examples and their general properties. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2942 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/3453 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | eng |
dc.subject.other | Dissipation distance | eng |
dc.subject.other | geodesic curves | eng |
dc.subject.other | cone space | eng |
dc.subject.other | optimal transport | eng |
dc.subject.other | Onsager operator | eng |
dc.subject.other | reaction-diffusion equations | eng |
dc.title | Optimal transport in competition with reaction: The Hellinger-Kantorovich distance and geodesic curves | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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