Abstract
<p style='text-indent:20px;'>A model of irrigation network, where lower branches must be thicker in order to support the weight of the higher ones, was recently introduced in [<xref ref-type="bibr" rid="b7">7</xref>]. This leads to a countable family of ODEs, describing the thickness of every branch, solved by backward induction. The present paper determines what kind of measures can be irrigated with a finite weighted cost. Indeed, the boundedness of the cost depends on the dimension of the support of the irrigated measure, and also on the asymptotic properties of the ODE which determines the thickness of branches.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Computer Science Applications,General Engineering,Statistics and Probability,Applied Mathematics,Computer Science Applications,General Engineering,Statistics and Probability
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