Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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.


References [Enhancements On Off] (What's this?)

  • [1] G.I. Ågren and E. Bosatta, Quality: A bridge between theory and experiment in soil organic matter studies, Oikos 76 (1996), no. 3, 522-528.
  • [2] -, Theoretical ecosystem ecology: Understanding element cycles, Cambridge University Press, 1998.
  • [3] G.I. Ågren, E. Bosatta, and J. Balesdent, Isotope discrimination during decomposition of organic matter: A theoretical analysis, Soil Science Society of America Journal 60 (1996), no. 4, 1121-1126.
  • [4] E. Bosatta and G.I. Ågren, Theoretical analyses of decomposition of heterogeneous substrates, Soil Biology and Biochemistry 17 (1985), no. 5, 601-610.
  • [5] -, Dynamics of carbon and nitrogen in the organic-matter of the soil - a generic theory, American Naturalist 138 (1991), no. 1, 227-245.
  • [6] -, Theoretical-analysis of microbial biomass dynamics in soils, Soil Biology and Biochemistry 26 (1994), no. 1, 143-148.
  • [7] -, Theoretical analyses of carbon and nutrient dynamics in soil profiles, Soil Biology and Biochemistry 28 (1996), no. 10-11, 1523-1531.
  • [8] -, Quality and irreversibility: constraints on ecosystem development, Proceedings of the Royal Society of London Series B-Biological Sciences 269 (2002), no. 1487, 203-210.
  • [9] Ernesto Bosatta and Göran I. Ågren, Exact solutions to the continuous-quality equation for soil organic matter turnover, J. Theoret. Biol. 224 (2003), no. 1, 97–105. MR 2069252, https://doi.org/10.1016/S0022-5193(03)00147-4
  • [10] Henri Cartan, Calcul différentiel, Hermann, Paris, 1967 (French). MR 0223194
  • [11] Pierre Colmez, Éléments d’analyse et d’algèbre (et de théorie des nombres), Éditions de l’École Polytechnique, Palaiseau, 2009 (French). MR 2583834
  • [12] Klaus Deimling, Ordinary differential equations in Banach spaces, Lecture Notes in Mathematics, Vol. 596, Springer-Verlag, Berlin-New York, 1977. MR 0463601
  • [13] J.P. Demailly, Analyse numérique et équations différentielles, Collection Grenoble sciences, EDP sciences, 2006.
  • [14] D. Derrien and W. Amelung, Computing the mean residence time of soil carbon fractions using stable isotopes: impacts of the model framework, European Journal of Soil Science 62 (2011), no. 2, 237-252.
  • [15] J. Dieudonné, Fondements de l’analyse moderne, Traduit de l’anglais par D. Huet. Avant-propos de G. Julia. Cahiers Scientifiques, Fasc. XXVIII, Gauthier-Villars, Éditeur, Paris, 1963 (French). MR 0161945
  • [16] Serge Lang, Real analysis, 2nd ed., Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1983. MR 783635
  • [17] R. Levins, The strategy of model building in population biology, American Scientist 54 (1966), no. 4, 421-431.
  • [18] S. Manzoni and A. Porporato, Soil carbon and nitrogen mineralization: Theory and models across scales, Soil Biology and Biochemistry 41 (2009), no. 7, 1355-1379.
  • [19] Benoît Perthame, Transport equations in biology, Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2007. MR 2270822

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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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