Root growth: homogenization in domains with time dependent partial perforations

Yves Capdeboscq, Mariya Ptashnyk

    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 - 2012


    • Homogenization
    • time dependent domains
    • root growth


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