Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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

Authors: Göran I. Ågren, Matthieu Barrandon, Laurent Saint-André and Julien Sainte-Marie
Journal: Quart. Appl. Math. 75 (2017), 131-153
MSC (2010): Primary 35R09, 92F99; Secondary 65M06, 45K05
DOI: https://doi.org/10.1090/qam/1438
Published electronically: August 24, 2016
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Abstract: 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\in \mathbb{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.

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Additional Information

Göran I. Ågren
Affiliation: Department of Ecology, Swedish University of Agricultural Sciences, S-75007 Uppsala, Sweden
Email: goran.agren@slu.se

Matthieu Barrandon
Affiliation: Institut Elie Cartan, Université de Lorraine, F-54506 Vandoeuvre-lès-Nancy, France
Email: matthieu.barrandon@univ-lorraine.fr

Laurent Saint-André
Affiliation: Biogéochimie des Ecosystèmes Forestiers, Institut National de la Recherche Agronomique, F-54280 Champenoux, France
Email: st-andre@nancy.inra.fr

Julien Sainte-Marie
Affiliation: Biogéochimie des Ecosystèmes Forestiers, Institut National de la Recherche Agronomique, F-54280 Champenoux, France
Email: juliensaintemarie@gmail.com

DOI: https://doi.org/10.1090/qam/1438
Keywords: Soil organic matter, integro-differential equations, ordinary differential equations on Banach spaces, decomposition model
Received by editor(s): January 5, 2016
Published electronically: August 24, 2016
Article copyright: © Copyright 2016 Brown University

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