Weak Solutions for a Hyperbolic System with Unilateral Constraint and Mass Loss
نویسنده
چکیده
We consider isentropic gas dynamics equations with unilateral constraint on the density and mass loss. The 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. Solutions faibles pour un syt eme hyperbolique avec contrainte unilat erale et perte de masse Nous consid erons les equations de la dynamique des gaz isentropique avec con-trainte unilat erale sur la densit e et perte de masse. Les lois de pression et sans pression sont consid er ees. Nous proposons une formulation faible entropique du sys-t eme qui incorpore la contrainte et le multiplicateur de Lagrange, pour laquelle nous montrons la stabilit e faible et l'existence de solutions. Le mod ele avec pression non nulle est approch e par un mod ele de relaxation BGK cin etique, tandis que le mod ele sans pression est approch e par une dynamique de bouchons collants avec perte de masse.
منابع مشابه
Weak solutions for a hyperbolic system withunilateral constraint and mass
We consider isentropic gas dynamics equations with unilateral constraint on the density and mass loss. The 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...
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