A NON-STANDARD FREE BOUNDARY PROBLEM ARISING FROM STRATIGRAPHY
S. N. Antont︠s︡ev, Gérard Gagneux, Robert Luce, Guy Vallet · Analysis and Applications · 2006
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.