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.

Keywords: homogenization, root growth, time dependent domains

@article{COCV_2012__18_3_856_0, author = {Capdeboscq, Yves and Ptashnyk, Mariya}, 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}, volume = {18}, number = {3}, year = {2012}, doi = {10.1051/cocv/2011184}, mrnumber = {3041667}, zbl = {1259.35023}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2011184/} }

TY - JOUR AU - Capdeboscq, Yves AU - Ptashnyk, Mariya TI - Root growth: homogenization in domains with time dependent partial perforations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 856 EP - 876 VL - 18 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2011184/ DO - 10.1051/cocv/2011184 LA - en ID - COCV_2012__18_3_856_0 ER -

%0 Journal Article %A Capdeboscq, Yves %A Ptashnyk, Mariya %T Root growth: homogenization in domains with time dependent partial perforations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 856-876 %V 18 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2011184/ %R 10.1051/cocv/2011184 %G en %F COCV_2012__18_3_856_0

Capdeboscq, Yves; Ptashnyk, Mariya. Root growth: homogenization in domains with time dependent partial perforations. ESAIM: Control, Optimisation and Calculus of Variations, Volume 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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