A singular initial value problem to construct density-equalizing maps

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Document typeResearch report
Defense date2011-05
Rights accessOpen Access
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.
CitationAvinyó, A.; De Solà-Morales, J.; València, M. "A singular initial value problem to construct density-equalizing maps". 2011.
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