One-dimensional granular system with memory effects

C. Perrin (1) , M Westdickenberg (2)

1 I2M - Institut de Mathématiques de Marseille
2 Institut fur Mathematik, RWTH Aachen Univers

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.

Mots clés: pressureless gas dynamics; Granular flows

Domaines: Equations aux dérivées partielles [math.AP]

C. Perrin, M Westdickenberg. One-dimensional granular system with memory effects. SIAM Journal on Mathematical Analysis, 2018, 50 (6), pp.5921-5946. ⟨10.1137/17M1121421⟩. ⟨hal-01884376⟩