Existence and Uniqueness of a Weak Solution to a Stratigraphic Model

Robert Eymard (), Thierry Gallouët (), Véronique Gervais () and Roland Masson ()
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Robert Eymard: Université de Marne-La-Vallée, Dépt de Mathématiques
Thierry Gallouët: LATP, Université de Provence
Véronique Gervais: Institut Français du Pétrole
Roland Masson: Institut Français du Pétrole

A chapter in Numerical Mathematics and Advanced Applications, 2004, pp 278-287 from Springer

Abstract: 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 i s 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 i s with a linear advection equation for the basin concentration, for which c i s 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.

Keywords: Weak Solution; Surface Concentration; Foreland Basin; Adjoint Problem; Linear Parabolic Equation (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18775-9_25

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DOI: 10.1007/978-3-642-18775-9_25

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