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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

Authors' information

Swedish University of Agricultural Sciences, Department of Ecology
Barrandon, Matthieu
University of Lorraine
Saint-André, Laurent
National Institute of Agricultural Research (INRA)
Sainte-Marie, Julien
National Institute of Agricultural Research (INRA)

UKÄ Subject classification

Soil Science
Mathematical Analysis

Publication Identifiers


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