In this paper we study the well-posedness for a scalar conservation law in which the flux term is non-local in space. This equation represents a reduced model for slow erosion in granular flow ([1,6]) and describes roughly the evolution of a profile of stationary matter, under the effect of a thin moving layer of granular matter on the top of it. We show that the present equation admits weak solutions existing globally in time and prove their stability w.r.t the initial data. These properties are related to the assumption on the erosion flux. Different assumptions may lead to significantly different behaviors, see [9].
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