Summary
In this paper, we study a multi-lithology diffusion model used to simulate the evolution through time of a sedimentary basin composed of several lithologies such as sand or shale. It is a simplified model for which the surficial flux in lithology i is taken proportional to the slope and to a lithology fraction c s i in lithology i at the top of the basin with a unitary diffusion coefficient. Thus, the sediment thickness variable satisfies a linear parabolic problem and decouples from the other unknowns. The remaining equations couple, for each lithology, a first order linear equation for the surface concentration c s i with a linear advection equation for the basin concentration, for which c s i appears as an input boundary condition at the top of the basin in case of sedimentation. The existence and uniqueness of a weak solution in L ∞ is proved for this problem.
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References
Eymard, R., Gallouët, T., Gervais, V., Masson, R.(submitted 2003): Convergence of a numerical scheme for stratigraphic modeling. SIAM J. Num. Anal.
Eymard, R., Gallouët, T., Granjeon, D., Masson, R., Tran, Q.(2003): Multilithology stratigraphic model under maximum erosion rate constraint. Int. J. of Num. Methods in Eng., (to appear)
Eymard, R., Gallouët, T., Herbin, R.(2000): The Finite Volume Method. In Ciarlet P. and Lions J.(eds.) Handbook of Numerical Analysis, 7. Elsevier
Flemings, P.B., Jordan, T.E.(1989): A Synthetic Stratigraphic Model of Foreland Basin Development. J. of Geophysical Research, Vol 94, B4, 3851–3866
Godlewski, E., Raviart, P.(1996): Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer
Granjeon, D.,(1997): Modélisation stratigraphique déterministe; conception et applications d’un modèle diffusif 3D multilithologique. Ph. D. dissertation, Gosciences Rennes, Rennes, France
Rivenaes, J.C.(1992): Application of a dual lithology, depth-dependent diffusion equation in stratigraphic simulation. Basin Research, 4, 133–146
Tucker, G.E., Slingerland, R.L.(1994): Erosional dynamics, flexural isostasy, and long-lived escarpments: A numerical modeling study. J. of Geophysical Research, Vol 99, B6, 12,229–12,243
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Eymard, R., Gallouët, T., Gervais, V., Masson, R. (2004). Existence and Uniqueness of a Weak Solution to a Stratigraphic Model. In: Feistauer, M., Dolejší, V., Knobloch, P., Najzar, K. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18775-9_25
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DOI: https://doi.org/10.1007/978-3-642-18775-9_25
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