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Existence and Uniqueness of a Weak Solution to a Stratigraphic Model

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • 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)

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.

Suggested Citation

  • Robert Eymard & Thierry Gallouët & Véronique Gervais & Roland Masson, 2004. "Existence and Uniqueness of a Weak Solution to a Stratigraphic Model," Springer Books, in: Miloslav Feistauer & Vít Dolejší & Petr Knobloch & Karel Najzar (ed.), Numerical Mathematics and Advanced Applications, pages 278-287, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18775-9_25
    DOI: 10.1007/978-3-642-18775-9_25
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