Volume 18, Number 3, July-September 2012
|Page(s)||856 - 876|
|Published online||14 October 2011|
Root growth: homogenization in domains with time dependent partial perforations
Mathematical Institute, 24-29 St Giles', Oxford
Department of Mathematics I, RWTH Aachen University, Wüllnerstr. 5b, 52056 Aachen, Germany
Received: 28 October 2010
Revised: 27 June 2011
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.
Mathematics Subject Classification: 35B27 / 35K55 / 92C99s
Key words: Homogenization / root growth / time dependent domains
© EDP Sciences, SMAI, 2011
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