Root growth: Homogenization in domains with time dependent partial perforations

Yves Capdeboscq*, Mariya Ptashnyk

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)856-876
Number of pages21
JournalESAIM - Control, Optimisation and Calculus of Variations
Issue number3
Publication statusPublished - Jul 2012


  • Homogenization
  • Root growth
  • Time dependent domains

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics


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