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dc.contributor.authorAvinyó Andrés, Albert
dc.contributor.authorSolà-Morales Rubió, Joan de
dc.contributor.authorValència Guitart, Marta
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2012-02-21T11:34:18Z
dc.date.available2012-02-21T11:34:18Z
dc.date.created2011-05
dc.date.issued2011-05
dc.identifier.citationAvinyó, A.; De Solà-Morales, J.; València, M. "A singular initial value problem to construct density-equalizing maps". 2011.
dc.identifier.urihttp://hdl.handle.net/2117/15276
dc.description.abstractThe diffusion-based algorithm to produce density-equalizing maps interprets diffusion as an advection process. This algorithm uses the dynamics of a flow that is defined by an initial value problem that turns out to be very singular at the initial time. The singularities appear when the initial density has line or angle discontinuities, which is always the case, for example, in area cartogram maps. This singular initial value problem is analyzed mathematically in this paper and the conclusion is that despite these singularities, it has a unique solution. This justifies the extensive numerical use of this algorithm in the recent years. The techniques presented in this paper use both partial and ordinary differential equations estimates.
dc.format.extent8 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshDifferential equations
dc.titleA singular initial value problem to construct density-equalizing maps
dc.typeExternal research report
dc.subject.lemacEquacions diferencials
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.rights.accessOpen Access
local.identifier.drac9791395
dc.description.versionPreprint
local.citation.authorAvinyó, A.; De Solà-Morales, J.; València, M.
local.citation.publicationNameA singular initial value problem to construct density-equalizing maps


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Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain