  We consider a hybrid compressible/incompressible system with memory effects
introduced by Lefebvre Lepot and Maury (2011) for the description of
one-dimensional granular flows. We prove a first global existence result for
this system without additional viscous dissipation. Our approach extends the
one by Cavalletti, Sedjro, Westdickenberg (2015) for the pressureless Euler
system to the constraint granular case with memory effects. We construct
Lagrangian solutions based on an explicit formula of the monotone rearrangement
associated to the density and explain how the memory effects are linked to the
external constraints imposed on the flow. This result is finally extended to a
heterogeneous maximal density constraint depending on time and space.
