Weak solutions for a hyperbolic system with unilateral constraint and mass loss
Berthelin, F ; Bouchut, F
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003), p. 975-997 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_2003__20_6_975_0,
     author = {Berthelin, Florent and Bouchut, Fran\c cois},
     title = {Weak solutions for a hyperbolic system with unilateral constraint and mass loss},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {20},
     year = {2003},
     pages = {975-997},
     doi = {10.1016/S0294-1449(03)00012-X},
     mrnumber = {2008686},
     zbl = {1079.76063},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2003__20_6_975_0}
}

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) pp. 975-997. doi : 10.1016/S0294-1449(03)00012-X. http://gdmltest.u-ga.fr/item/AIHPC_2003__20_6_975_0/

[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 1425004 | Zbl 0631.47038

[2] Berthelin F, Existence and weak stability for a pressureless model with unilateral constraint, Math. Models Methods Appl. Sci. 12 (2002) 249-272. | MR 1892581 | Zbl 1027.35079

[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 1838140 | Zbl 1006.82023

[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 1938602 | Zbl 1032.76064

[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 1323183 | Zbl 0863.76068

[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 1705583 | Zbl 0957.82028

[7] Bouchut F, Renormalized solutions to the Vlasov equation with coefficients of bounded variation, Arch. Ration. Mech. Anal. 157 (2001) 75-90. | MR 1822415 | Zbl 0979.35032

[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 1799394 | Zbl 0998.76088

[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 1720754 | Zbl 0937.35098

[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 1766512 | Zbl 0973.35057

[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 1614638 | Zbl 0893.35068

[12] Brenier Y, Grenier E, Sticky particles and scalar consevation laws, SIAM J. Numer. Anal. 35 (1998) 2317-2328. | MR 1655848 | Zbl 0924.35080

[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 1127927 | Zbl 0763.35014

[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 1384139 | Zbl 0852.35097

[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 912215 | Zbl 0629.76109

[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 1345441 | Zbl 0837.35088

[18] Lévi L, Problèmes unilatéraux pour des équations non linéaires de convection-réaction, Ann. Fac. Sci. Toulouse Math. 4 (1995) 593-631. | Numdam | MR 1607514 | Zbl 0861.35058

[19] Lévi L, Obstacle problems for scalar conservation laws, M2AN Math. Model. Numer. Anal. 35 (2001) 575-593. | Numdam | MR 1837085 | Zbl 0990.35096

[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 1687274 | Zbl 0917.76073

[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 1383202 | Zbl 0853.76077

[22] Mignot F, Puel J.-P, Inéquations variationnelles et quasivariationnelles hyperboliques du premier ordre, J. Math. Pures Appl. (9) 55 (1976) 353-378. | MR 499769 | Zbl 0359.35050

[23] Perthame B, Tadmor E, A kinetic equation with kinetic entropy functions for scalar conservation laws, Comm. Math. Phys. 136 (1991) 501-517. | MR 1099693 | Zbl 0729.76070

[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 1753092 | Zbl 0963.35117

[25] Vasseur A, Kinetic semidiscretization of scalar conservation laws and convergence by using averaging lemmas, SIAM J. Numer. Anal. 36 (1999) 465-474. | MR 1668278 | Zbl 0920.65060

[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 1020.65054