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Article Dans Une Revue Analysis and Applications Année : 2011

A NON-STANDARD FREE BOUNDARY PROBLEM ARISING FROM STRATIGRAPHY

Résumé

In this paper, we are interested in the mathematical analysis of a geological stratigraphic model, taking into account a limited weathering condition. Firstly, we present the physical model and the mathematical formulation, which lead to an original locally hyperbolic conservation law. Then, after some heuristic simplifications, the definition of a solution and some mathematical tools in order to resolve the problem are given. Within the framework of sedimentation processes, we illustrate in the 1-D case the changing type of the equation: hyperbolic with finite speed propagation and parabolic with diffusive comportment or stationary. At the end, we present some open problems related to free boundary phenomena.
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hal-04312944 , version 1 (28-11-2023)

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S. Antontsev, G. Gagneux, R. Luce, Guy Vallet. A NON-STANDARD FREE BOUNDARY PROBLEM ARISING FROM STRATIGRAPHY. Analysis and Applications, 2011, 04 (03), pp.209-236. ⟨10.1142/S0219530506000759⟩. ⟨hal-04312944⟩
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