Abstract:
We consider isentropic gas dynamics equations
with unilateral constraint on the density and mass loss. The $\gamma$ and
pressureless pressure laws are considered. We propose an entropy weak formulation
of the system that incorporates the constraint and Lagrange multiplier,
for which we prove weak stability and existence of solutions. The nonzero
pressure model
is approximated by a kinetic BGK relaxation model,
while the pressureless model is approximated by a sticky-blocks dynamics
with mass loss.