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Séminaire du LJLL - 04 06 2021 14h00 : L. Caravenna

04 juin 2021 — 14h00
Exposé à distance retransmis par Zoom
Laura Caravenna (Université de Padoue)
On the L^1 stability of BV solutions in a model of granular flow
Résumé
The evolution of a granular material, with slow erosion and deposition, can be framed mathematically with very different tools. We study a model that describes it as a 2×2 system of hyperbolic balance laws in terms of the thickness of a moving layer on the top and of a standing layer at the bottom. The characteristic speeds of such systems are neither linearly degenerate nor genuinely nonlinear, making it challenging.
We shall briefly introduce the model and discuss the L^1-stability of solutions, relying on the construction of a Lyapunov-like functional equivalent to the L^1-distance. Global existence of entropy weak solutions was established by Amadori and Shen in 2009 for initial data with bounded but possibly large total variation, under the assumption of small initial height of the moving layer. The Lyapunov functional we introduce is in the spirit of the functional introduced 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.