@article{AFST_2000_6_9_4_605_0, author = {Florent Berthelin and Fran\c{c}ois Bouchut}, 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}, zbl = {1006.82023}, mrnumber = {1838140}, language = {en}, url = {https://afst.centre-mersenne.org/item/AFST_2000_6_9_4_605_0/} }
TY - JOUR AU - Florent Berthelin AU - François Bouchut TI - Solution with finite energy to a BGK system relaxing to isentropic gas dynamics JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2000 SP - 605 EP - 630 VL - 9 IS - 4 PB - Université Paul Sabatier. Faculté des sciences PP - Toulouse UR - https://afst.centre-mersenne.org/item/AFST_2000_6_9_4_605_0/ LA - en ID - AFST_2000_6_9_4_605_0 ER -
%0 Journal Article %A Florent Berthelin %A François Bouchut %T Solution with finite energy to a BGK system relaxing to isentropic gas dynamics %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2000 %P 605-630 %V 9 %N 4 %I Université Paul Sabatier. Faculté des sciences %C Toulouse %U https://afst.centre-mersenne.org/item/AFST_2000_6_9_4_605_0/ %G en %F AFST_2000_6_9_4_605_0
Florent Berthelin; François Bouchut. 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. https://afst.centre-mersenne.org/item/AFST_2000_6_9_4_605_0/
[1] Discrete kinetic schemes for multidimensional systems of conservation laws, SIAM J. Numer. Anal. 37 (2000), 1973-2004. | MR | Zbl
), ). -[2] Kinetic invariant domains and relaxation limit from a BGK model to isentropic gas dynamics, to appear in Asymptotic Analysis. | MR | Zbl
), ). -[3] 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] Averaged multivalued solutions for scalar conservation laws, SIAM J. Numer. Anal. 21 (1984), 1013-1037. | MR | Zbl
). -[5] 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] Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math. 47 (1994), 787-830. | MR | Zbl
), ), ). -[7] Convergence of the viscosity method for isentropic gas dynamics, Comm. Math. Phys. 91 (1983), 1-30. | MR | Zbl
). -[8] Regularity of the moments of the solution of a transport equation, J. Funct. Anal., 76, (1988), 110-125. | MR | Zbl
), ), ), ). -[9] The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math. 48 (1995), 235-276. | MR | Zbl
), ). -[10] 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] A kinetic formulation of multidimensional scalar conservation laws and related equations, J. Amer. Math. Soc. 7 (1994), 169-191. | MR | Zbl
), ), ). -[12] Kinetic formulation of the isentropic gas dynamics and p-systems, Comm. Math. Phys. 163 (1994), 415-431. | MR | Zbl
), ), ). -[13] A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws, J. Diff. Eq. 148 (1998), 292-317. | MR | Zbl
). -[14] 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] Global existence to the BGK model of Boltzmann equation, J. Diff. Eq. 82 (1989), 191-205. | MR | Zbl
). -[16] Weighted L∞ bounds and uniqueness for the Boltzmann BGK model, Arch. Rational Mech. Anal. 125 (1993), 289-295. | MR | Zbl
), ). -[17] A kinetic equation with kinetic entropy functions for scalar conservation laws, Comm. Math. Phys. 136 (1991), 501-517. | MR | Zbl
), ). -[18] 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
). -