A Conservation Law with Nonlocal Flux for Erosion Profiles
نویسندگان
چکیده
In this paper we review some results on a model for the erosion of mountain profile caused by small avalanches. The equation is a scalar conservation law with a non-local flux. Under suitable assumptions on the erosion rate, the mountain profile develops three types of singularities, namely kinks, shocks and hyper-kinks. Entropy weak solutions to the Cauchy problem can be constructed globally in time, taking limits of piecewise affine approximate solutions. Pairs of entropy and entropy flux functions are introduced, and the Lax admissibility condition is established.
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