9 research outputs found
One-dimensional granular system with memory effects
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
A simple proof of global existence for the 1D pressureless gas dynamics equations
Sticky particle solutions to the one-dimensional pressureless gas dynamics equations can be constructed by a suitable metric projection onto the cone of monotone maps, as was shown in recent work by Natile and Savaré. Their proof uses a discrete particle approximation and stability properties for first-order differential inclusions. Here we give a more direct proof that relies on a result by Haraux on the differentiability of metric projections. We apply the same method also to the one-dimensional Euler-Poisson system, obtaining a new proof for the global existence of weak solutions. © 2015 Society for Industrial and Applied Mathematics