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Research article - Peer-reviewed, 2017

Analysis of integro-differential equations modeling the vertical decomposition of soil organic matter

Agren, Goran I.; Barrandon, Matthieu; Saint-Andre, Laurent; Sainte-Marie, Julien


In this paper, a family of first-order hyperbolic integro-differential equations introduced to model the decomposition of organic matter (OM) are studied. These original equations depend on an extra variable named "quality". We prove that these equations admit solutions in particular Banach spaces ensuring the continuity and the N-order closure of equations (N is an element of N*) according to "quality". We first give a result of existence, uniqueness and smoothness in a general framework. Then, this result is applied to specific transport equations. Finally, a numerical illustration of solutions properties is given by using an implicit-explicit finite difference scheme.


Soil organic matter; integro-differential equations; ordinary differential equations on Banach spaces; decomposition model

Published in

Quarterly of Applied Mathematics
2017, Volume: 75, number: 1, pages: 131-153

    UKÄ Subject classification

    Soil Science
    Mathematical Analysis

    Publication identifier


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