no. 4
Solution with finite energy to a BGK system relaxing to isentropic gas dynamics
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 9 (2000) no. 4, pp. 605-630. 
@article{AFST_2000_6_9_4_605_0,
     author = {Berthelin, Florent and Bouchut, Fran\c{c}ois},
     title = {Solution with finite energy to a {BGK} system relaxing to isentropic gas dynamics},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {605--630},
     publisher = {Universit\'e Paul Sabatier. Facult\'e des sciences},
     address = {Toulouse},
     volume = {Ser. 6, 9},
     number = {4},
     year = {2000},
     mrnumber = {1838140},
     zbl = {1006.82023},
     language = {en},
     url = {http://archive.numdam.org/item/AFST_2000_6_9_4_605_0/}
}
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Berthelin, Florent; Bouchut, François. Solution with finite energy to a BGK system relaxing to isentropic gas dynamics. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 9 (2000) no. 4, pp. 605-630. http://archive.numdam.org/item/AFST_2000_6_9_4_605_0/

[1] Aregba-Driollet (D.), Natalini (R.). - Discrete kinetic schemes for multidimensional systems of conservation laws, SIAM J. Numer. Anal. 37 (2000), 1973-2004. | MR | Zbl

[2] Berthelin (F.), Bouchut (F.). - Kinetic invariant domains and relaxation limit from a BGK model to isentropic gas dynamics, to appear in Asymptotic Analysis. | MR | Zbl

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

[4] Brenier (Y.). - Averaged multivalued solutions for scalar conservation laws, SIAM J. Numer. Anal. 21 (1984), 1013-1037. | MR | Zbl

[5] 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

[6] Chen (G.Q.), Levermore (C.D.), Liu (T.-P.). - Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math. 47 (1994), 787-830. | MR | Zbl

[7] Diperna (R.J.). - Convergence of the viscosity method for isentropic gas dynamics, Comm. Math. Phys. 91 (1983), 1-30. | MR | Zbl

[8] Golse (F.), Lions (P.-L.), Perthame (B.), Sentis (R.). - Regularity of the moments of the solution of a transport equation, J. Funct. Anal., 76, (1988), 110-125. | MR | Zbl

[9] Jin (S.), Xin (Z.-P.). - The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math. 48 (1995), 235-276. | MR | Zbl

[10] 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

[11] Lions (P.-L.), Perthame (B.), Tadmor (E.). - A kinetic formulation of multidimensional scalar conservation laws and related equations, J. Amer. Math. Soc. 7 (1994), 169-191. | MR | Zbl

[12] Lions (P.-L.), Perthame (B.), Tadmor (E.). - Kinetic formulation of the isentropic gas dynamics and p-systems, Comm. Math. Phys. 163 (1994), 415-431. | MR | Zbl

[13] Natalini (R.). - A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws, J. Diff. Eq. 148 (1998), 292-317. | MR | Zbl

[14] Natalini (R.). - Recent results on hyperbolic relaxation problems. Analysis of systems of conservation laws (Aachen, 1997), 128-198. Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math., 99, Chapman & Hall/CRC, Boca Raton, FL, 1999. | Zbl

[15] Perthame (B.). - Global existence to the BGK model of Boltzmann equation, J. Diff. Eq. 82 (1989), 191-205. | MR | Zbl

[16] Perthame (B.), Pulvirenti (M.). - Weighted L∞ bounds and uniqueness for the Boltzmann BGK model, Arch. Rational Mech. Anal. 125 (1993), 289-295. | MR | Zbl

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

[18] 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