A 2-dimensional shape optimization problem for tree branches

Alberto Bressan; Sondre Tesdal Galtung; Alberto Bressan; Sondre Tesdal Galtung

doi:10.3934/nhm.2020031

Networks and Heterogeneous Media

2021, Volume 16, Issue 1: 1-29. doi: 10.3934/nhm.2020031

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A 2-dimensional shape optimization problem for tree branches

Alberto Bressan ^{1
,
,},
Sondre Tesdal Galtung ^{2
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1.
Department of Mathematics, Penn State University, University Park, PA 16802, USA
2.
Department of Mathematical Sciences, NTNU – Norwegian University of Science and Technology, NO-7491 Trondheim, Norway

Received: 01 June 2020 Revised: 01 September 2020 Published: 30 October 2020
49Q10, 49Q20

The paper is concerned with a shape optimization problem, where the functional to be maximized describes the total sunlight collected by a distribution of tree leaves, minus the cost for transporting water and nutrient from the base of trunk to all the leaves. In a 2-dimensional setting, the solution is proved to be unique and explicitly determined.
- Shape optimization,
- Sunlight functional,
- branched transport
Citation: Alberto Bressan, Sondre Tesdal Galtung. A 2-dimensional shape optimization problem for tree branches[J]. Networks and Heterogeneous Media, 2021, 16(1): 1-29. doi: 10.3934/nhm.2020031

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Abstract

The paper is concerned with a shape optimization problem, where the functional to be maximized describes the total sunlight collected by a distribution of tree leaves, minus the cost for transporting water and nutrient from the base of trunk to all the leaves. In a 2-dimensional setting, the solution is proved to be unique and explicitly determined.

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