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Root growth: homogenization in domains with time dependent partial perforations

Published online by Cambridge University Press:  14 October 2011

Yves Capdeboscq  and
Mariya Ptashnyk
Yves Capdeboscq
Affiliation:
Mathematical Institute, 24-29 St Giles', Oxford OX1 3LB, UK. capdeboscq@maths.ox.ac.uk
Mariya Ptashnyk
Affiliation:
Department of Mathematics I, RWTH Aachen University, Wüllnerstr. 5b, 52056 Aachen, Germany; ptashnyk@math1.rwth-aachen.de
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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.

Keywords

Homogenizationroot growthtime dependent domains
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 3 , July 2012 , pp. 856 - 876
Copyright
© EDP Sciences, SMAI, 2011

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