A Partial Differential Inequality in Geological Models

Abstract

Sedimentation and erosion processes in sedimentary basins can be modeled by a parabolic equation with a limiter on the fluxes and a constraint on the time variation. This limiter happens to satisfy a stationary scalar hyperbolic inequality, within a constraint, for which the authors prove the existence and the uniqueness of the solution. Actually, this solution is shown to be the maximal element of a convenient convex set of functions. The existence proof is obtained thanks to the use of a numerical scheme.

Keywords

Hyperbolic inequalities / Erosion and sedimentation models / 76S05 / 35K57 / 65N30 / 76M12

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