Root growth: homogenization in domains with time dependent partial perforations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 856-876.

In this article we derive a macroscopic model for the time evolution of root density, starting from a discrete mesh of roots, using homogenization techniques. In the microscopic model each root grows vertically according to an ordinary differential equation. The roots growth rates depend on the spatial distribution of nutrient in the soil, which also evolves in time, leading to a fully coupled non-linear problem. We derive an effective partial differential equation for the root tip surface and for the nutrient density.

DOI : 10.1051/cocv/2011184
Classification : 35B27, 35K55, 92C99s
Mots clés : homogenization, root growth, time dependent domains
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     title = {Root growth: homogenization in domains with time dependent partial perforations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {856--876},
     publisher = {EDP-Sciences},
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Capdeboscq, Yves; Ptashnyk, Mariya. Root growth: homogenization in domains with time dependent partial perforations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 856-876. doi : 10.1051/cocv/2011184. http://archive.numdam.org/articles/10.1051/cocv/2011184/

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