Optimal shapes for tree roots
Journal article
Submitted version
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https://hdl.handle.net/11250/3053037Utgivelsesdato
2022Metadata
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- Institutt for matematiske fag [2353]
- Publikasjoner fra CRIStin - NTNU [37221]
Sammendrag
The paper studies a class of variational problems, modeling optimal shapes for tree roots. Given a measure μ
describing the distribution of root hair cells, we seek to maximize a harvest functional H
, computing the total amount of water and nutrients gathered by the roots subject to a cost for transporting these nutrients from the roots to the trunk. Earlier papers have established the existence of an optimal measure and a priori bounds. Here we derive necessary conditions for optimality. Moreover, in space dimension d=2
, we prove that the support of an optimal measure is nowhere dense.