# Root growth: homogenization in domains with time dependent partial perforations

Yves Capdeboscq; Mariya Ptashnyk

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 3, page 856-876
- ISSN: 1292-8119

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topCapdeboscq, Yves, and Ptashnyk, Mariya. "Root growth: homogenization in domains with time dependent partial perforations." ESAIM: Control, Optimisation and Calculus of Variations 18.3 (2012): 856-876. <http://eudml.org/doc/277819>.

@article{Capdeboscq2012,

abstract = {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. },

author = {Capdeboscq, Yves, Ptashnyk, Mariya},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Homogenization; root growth; time dependent domains; time-dependent boundaries; PDE-ODE system},

language = {eng},

month = {11},

number = {3},

pages = {856-876},

publisher = {EDP Sciences},

title = {Root growth: homogenization in domains with time dependent partial perforations},

url = {http://eudml.org/doc/277819},

volume = {18},

year = {2012},

}

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

DA - 2012/11//

PB - EDP Sciences

VL - 18

IS - 3

SP - 856

EP - 876

AB - 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.

LA - eng

KW - Homogenization; root growth; time dependent domains; time-dependent boundaries; PDE-ODE system

UR - http://eudml.org/doc/277819

ER -

## References

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