WEAK SOLUTIONS FOR A HYPERBOLIC SYSTEM WITH UNILATERAL CONSTRAINT AND MASS LOSS SOLUTIONS FAIBLES POUR UN SYTÈME

ABSTRACT. – We consider isentropic gas dynamics equations with unilateral constraint on the density and mass loss. The γ 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. 2003 Éditions scientifiques et médicales Elsevier SAS MSC: 76T10; 35L65; 35L85; 76N15; 35A3