dc.contributor.author Avinyó Andrés, Albert dc.contributor.author Solà-Morales Rubió, Joan de dc.contributor.author València Guitart, Marta dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I dc.date.accessioned 2012-02-21T11:34:18Z dc.date.available 2012-02-21T11:34:18Z dc.date.created 2011-05 dc.date.issued 2011-05 dc.identifier.citation Avinyó, A.; De Solà-Morales, J.; València, M. "A singular initial value problem to construct density-equalizing maps". 2011. dc.identifier.uri http://hdl.handle.net/2117/15276 dc.description.abstract The 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.extent 8 p. dc.language.iso eng dc.rights Attribution-NonCommercial-NoDerivs 3.0 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística dc.subject.lcsh Differential equations dc.title A singular initial value problem to construct density-equalizing maps dc.type External research report dc.subject.lemac Equacions diferencials dc.contributor.group Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions dc.rights.access Open Access local.identifier.drac 9791395 dc.description.version Preprint local.citation.author Avinyó, A.; De Solà-Morales, J.; València, M. local.citation.publicationName A singular initial value problem to construct density-equalizing maps
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