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An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation

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dc.contributor.author Bressan, Alberto en_US
dc.contributor.author Fonte, Massimo en_US
dc.date.accessioned 2005 en_US
dc.date.accessioned 2011-09-07T20:27:45Z
dc.date.available 2005 en_US
dc.date.available 2011-09-07T20:27:45Z
dc.date.issued 2005 en_US
dc.identifier.citation Methods Appl. Anal. 12 (2005) 191-219 en_US
dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/1719 en_US
dc.description.abstract In this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the entire space H1. Our solutions are conservative, in the sense that the total energy int[(u2 + u2x) dx] remains a.e. constant in time. Our new approach is based on a distance functional J(u, v), defined in terms of an optimal transportation problem, which satisfies d dtJ(u(t), v(t)) ≤ κ · J(u(t), v(t)) for every couple of solutions. Using this new distance functional, we can construct arbitrary solutions as the uniform limit of multi-peakon solutions, and prove a general uniqueness result. en_US
dc.format.extent 261370 bytes en_US
dc.format.mimetype application/pdf en_US
dc.language.iso en_US en_US
dc.relation.ispartofseries SISSA;27/2005/M en_US
dc.relation.ispartofseries arXiv.org;math.AP/0504450 en_US
dc.title An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation en_US
dc.type Preprint en_US
dc.contributor.department Functional Analysis and Applications en_US
dc.contributor.area Mathematics en_US


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