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ESAIM: Mathematical Modelling and Numerical Analysis (1)

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New unilateral problems in stratigraphy
Stanislav N. Antontsev, Gérard Gagneux, Robert Luce, Guy Vallet
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 40 / Issue 4 / July 2006

Published online by Cambridge University Press:

15 November 2006, pp. 765-784

Print publication:

July 2006
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This work deals with the study of some stratigraphic models for the formation of geological basins under a maximal erosion rate constrain. It leads to introduce differentialinclusions of degenerated hyperbolic-parabolic type $0\in \partial _{t}u-div\{H(\partial _{t}u+E)\nabla u\}$ , where H is the maximal monotonous graph of the Heaviside function and E is a given non-negative function. Firstly, we present the new and realistic models and an original mathematical formulation, taking into account the weather-limited rate constraint in the conservation law, with a unilateral constraint on the outflow boundary. Then, we give a study of the 1-D case with numerical illustrations.