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One-dimensional granular system with memory effects

Abstract : We consider a hybrid compressible/incompressible system with memory effects, introduced recently by Lefebvre Lepot and Maury for the description of one-dimensional granular flows. We prove a global existence result for this system without assuming additional viscous dissipation. Our approach extends the one by Cavalletti et al. for the pressureless Euler system to the constrained granular case with memory effects. We construct Lagrangian solutions based on an explicit formula using the monotone rearrangement associated to the density. We explain how the memory effects are linked to the external constraints imposed on the flow. This result can also be extended to a heterogeneous maximal density constraint depending on time and space.
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https://hal.archives-ouvertes.fr/hal-01884376
Contributor : Charlotte Perrin <>
Submitted on : Sunday, September 30, 2018 - 9:26:12 PM
Last modification on : Thursday, January 23, 2020 - 6:22:13 PM
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C. Perrin, M Westdickenberg. One-dimensional granular system with memory effects. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2018, 50 (6), pp.5921-5946. ⟨10.1137/17M1121421⟩. ⟨hal-01884376⟩

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