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
MathSciNet review:
3580098
Full-text PDF
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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
- 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.
- ---, Theoretical ecosystem ecology: Understanding element cycles, Cambridge University Press, 1998.
- 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.
- E. Bosatta and G.I. Ågren, Theoretical analyses of decomposition of heterogeneous substrates, Soil Biology and Biochemistry 17 (1985), no. 5, 601–610.
- ---, Dynamics of carbon and nitrogen in the organic-matter of the soil - a generic theory, American Naturalist 138 (1991), no. 1, 227–245.
- ---, Theoretical-analysis of microbial biomass dynamics in soils, Soil Biology and Biochemistry 26 (1994), no. 1, 143–148.
- ---, Theoretical analyses of carbon and nutrient dynamics in soil profiles, Soil Biology and Biochemistry 28 (1996), no. 10-11, 1523–1531.
- ---, Quality and irreversibility: constraints on ecosystem development, Proceedings of the Royal Society of London Series B-Biological Sciences 269 (2002), no. 1487, 203–210.
- 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, DOI https://doi.org/10.1016/S0022-5193%2803%2900147-4
- Henri Cartan, Calcul différentiel, Hermann, Paris, 1967 (French). MR 0223194
- Pierre Colmez, Éléments d’analyse et d’algèbre (et de théorie des nombres), Éditions de l’École Polytechnique, Palaiseau, 2009 (French). MR 2583834
- Klaus Deimling, Ordinary differential equations in Banach spaces, Lecture Notes in Mathematics, Vol. 596, Springer-Verlag, Berlin-New York, 1977. MR 0463601
- J.P. Demailly, Analyse numérique et équations différentielles, Collection Grenoble sciences, EDP sciences, 2006.
- 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.
- J. Dieudonné, Fondements de l’analyse moderne, Cahiers Scientifiques, Fasc. XXVIII, Gauthier-Villars, Éditeur, Paris, 1963 (French). Traduit de l’anglais par D. Huet. Avant-propos de G. Julia. MR 0161945
- Serge Lang, Real analysis, 2nd ed., Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1983. MR 783635
- R. Levins, The strategy of model building in population biology, American Scientist 54 (1966), no. 4, 421–431.
- 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.
- Benoît Perthame, Transport equations in biology, Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2007. MR 2270822
References
- 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.
- ---, Theoretical ecosystem ecology: Understanding element cycles, Cambridge University Press, 1998.
- 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.
- E. Bosatta and G.I. Ågren, Theoretical analyses of decomposition of heterogeneous substrates, Soil Biology and Biochemistry 17 (1985), no. 5, 601–610.
- ---, Dynamics of carbon and nitrogen in the organic-matter of the soil - a generic theory, American Naturalist 138 (1991), no. 1, 227–245.
- ---, Theoretical-analysis of microbial biomass dynamics in soils, Soil Biology and Biochemistry 26 (1994), no. 1, 143–148.
- ---, Theoretical analyses of carbon and nutrient dynamics in soil profiles, Soil Biology and Biochemistry 28 (1996), no. 10-11, 1523–1531.
- ---, Quality and irreversibility: constraints on ecosystem development, Proceedings of the Royal Society of London Series B-Biological Sciences 269 (2002), no. 1487, 203–210.
- 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, DOI https://doi.org/10.1016/S0022-5193%2803%2900147-4
- Henri Cartan, Calcul différentiel, Hermann, Paris, 1967 (French). MR 0223194
- Pierre Colmez, Éléments d’analyse et d’algèbre (et de théorie des nombres), Éditions de l’École Polytechnique, Palaiseau, 2009 (French). MR 2583834
- Klaus Deimling, Ordinary differential equations in Banach spaces, Lecture Notes in Mathematics, Vol. 596, Springer-Verlag, Berlin-New York, 1977. MR 0463601
- J.P. Demailly, Analyse numérique et équations différentielles, Collection Grenoble sciences, EDP sciences, 2006.
- 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.
- 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
- Serge Lang, Real analysis, 2nd ed., Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1983. MR 783635
- R. Levins, The strategy of model building in population biology, American Scientist 54 (1966), no. 4, 421–431.
- 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.
- 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
MR Author ID:
285642
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
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
