Weak solutions for a hyperbolic system with unilateral constraint and mass loss
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) no. 6, pp. 975-997. 
@article{AIHPC_2003__20_6_975_0,
     author = {Berthelin, F and Bouchut, F},
     title = {Weak solutions for a hyperbolic system with unilateral constraint and mass loss},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {975--997},
     publisher = {Elsevier},
     volume = {20},
     number = {6},
     year = {2003},
     doi = {10.1016/S0294-1449(03)00012-X},
     mrnumber = {2008686},
     zbl = {1079.76063},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S0294-1449(03)00012-X/}
}
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Berthelin, F; Bouchut, F. Weak solutions for a hyperbolic system with unilateral constraint and mass loss. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) no. 6, pp. 975-997. doi : 10.1016/S0294-1449(03)00012-X. http://www.numdam.org/articles/10.1016/S0294-1449(03)00012-X/

[1] Barthélemy L, Problème d'obstacle pour une équation quasi-linéaire du premier ordre, Ann. Fac. Sci. Toulouse Math. 9 (1988) 137-159. | Numdam | MR | Zbl

[2] Berthelin F, Existence and weak stability for a pressureless model with unilateral constraint, Math. Models Methods Appl. Sci. 12 (2002) 249-272. | MR | Zbl

[3] Berthelin F, Bouchut F, Solution with finite energy to a BGK system relaxing to isentropic gas dynamics, Ann. Fac. Sci. Toulouse 9 (2000) 605-630. | Numdam | MR | Zbl

[4] Berthelin F, Bouchut F, Kinetic invariant domains and relaxation limit from a BGK model to isentropic gas dynamics, Asymptotic Analysis 31 (2002) 153-176. | MR | Zbl

[5] Bouchut F, On zero pressure gas dynamics, in: Advances in Kinetic Theory and Computing, Ser. Adv. Math. Appl. Sci., 22, World Scientific, River Edge, NJ, 1994, pp. 171-190. | MR | Zbl

[6] Bouchut F, Construction of BGK models with a family of kinetic entropies for a given system of conservation laws, J. Stat. Phys. 95 (1999) 113-170. | MR | Zbl

[7] Bouchut F, Renormalized solutions to the Vlasov equation with coefficients of bounded variation, Arch. Ration. Mech. Anal. 157 (2001) 75-90. | MR | Zbl

[8] Bouchut F, Brenier Y, Cortes J, Ripoll J.-F, A hierarchy of models for two-phase flows, J. Nonlinear Sci. 10 (2000) 639-660. | MR | Zbl

[9] Bouchut F, James F, Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness, Comm. Partial Differential Equations 24 (1999) 2173-2189. | MR | Zbl

[10] Boudin L, A solution with bounded expansion rate to the model of viscous pressureless gases, SIAM J. Math. Anal. 32 (2000) 172-193. | MR | Zbl

[11] Brenier Y, Corrias L, A kinetic formulation for multi-branch entropy solutions of scalar conservation laws, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998) 169-190. | Numdam | MR | Zbl

[12] Brenier Y, Grenier E, Sticky particles and scalar consevation laws, SIAM J. Numer. Anal. 35 (1998) 2317-2328. | MR | Zbl

[13] B. Després, Equality or convex inequality constraints and hyperbolic systems of conservation laws with entropy, Preprint, 2001.

[14] Di Perna R.J, Lions P.-L, Meyer Y, Lp regularity of velocity averages, Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991) 271-287. | Numdam | MR | Zbl

[15] E W, Rykov Y.G, Sinai Y.G, Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics, Comm. Math. Phys. 177 (1996) 349-380. | MR | Zbl

[16] Gagneux G, Lefevère A.M, Madaune-Tort M, Une approche analytique d'un modèle black-oil des écoulements triphasiques compressibles en ingénierie pétrolière, J. Mécanique Théor. Appl. 6 (1987) 547-569. | MR | Zbl

[17] Grenier E, Existence globale pour le système des gaz sans pression, C. R. Acad. Sci. Paris Sér. I Math. 321 (2) (1995) 171-174. | MR | Zbl

[18] Lévi L, Problèmes unilatéraux pour des équations non linéaires de convection-réaction, Ann. Fac. Sci. Toulouse Math. 4 (1995) 593-631. | Numdam | MR | Zbl

[19] Lévi L, Obstacle problems for scalar conservation laws, M2AN Math. Model. Numer. Anal. 35 (2001) 575-593. | Numdam | MR | Zbl

[20] Lions P.-L, Masmoudi N, On a free boundary barotropic model, Ann. Inst. H. Poincaré Anal. Non linéaire 16 (1999) 373-410. | Numdam | MR | Zbl

[21] Lions P.-L, Perthame B, Souganidis P.E, Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates, Comm. Pure Appl. Math. 49 (1996) 599-638. | MR | Zbl

[22] Mignot F, Puel J.-P, Inéquations variationnelles et quasivariationnelles hyperboliques du premier ordre, J. Math. Pures Appl. (9) 55 (1976) 353-378. | MR | Zbl

[23] Perthame B, Tadmor E, A kinetic equation with kinetic entropy functions for scalar conservation laws, Comm. Math. Phys. 136 (1991) 501-517. | MR | Zbl

[24] Serre D, Relaxation semi-linéaire et cinétique des systèmes de lois de conservation, Ann. Inst. H. Poincaré Anal. Non linéaire 17 (2000) 169-192. | Numdam | MR | Zbl

[25] Vasseur A, Kinetic semidiscretization of scalar conservation laws and convergence by using averaging lemmas, SIAM J. Numer. Anal. 36 (1999) 465-474. | MR | Zbl

[26] Vasseur A, Convergence of a semi-discrete kinetic scheme for the system of isentropic gas dynamics with γ=3, Indiana Univ. Math. J. 48 (1999) 347-364. | Zbl

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