# On the L1 stability of BV solutions in a model of granular flow

## Abstract

I will discuss the problem of L1 stability for BV solution in an IBVP for a 2×2 system of hyperbolic balance laws modelling granular flow on a standing layer, of interest also for describing slow erosion of a mountain. Global existence of entropy weak solutions was established by Amadori and Shen in 2009-11 for initial data with bounded but possibly large total variation, under the assumption of small initial height of the moving layer. For this problem, we introduce a Lyapunov functional in the spirit of the one by Liu and Yang in 1999 and then developed by Bressan, Liu and Yang in 1999 for systems of conservation laws with genuinely nonlinear or linearly degenerate characteristic fields. In the singular limit of slow erosion, when the rolling layer is vanishingly thin, the profile of the mountain has been proved in 2011 by Amadori-Shen to be described by an integro-differential equation.

Joint work with F. Ancona (Padova) & C. Christoforou (Cyprus).

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