Kinetic invariant domains and relaxation limit from a BGK model to isentropic gas dynamics

Asymptotic Analysis

Volumn 31, Issue 2, 2002, Pages 153-176

  Berthelin, F ^a   Bouchut, F ^b  

^a UNIVERSITÉ D'ORLÉANS   (France)

^b ÉCOLE NORMALE SUPÉRIEURE   (France)

Author keywords

Isentropic gas dynamics; Kinetic BGK model; Kinetic entropy; Kinetic invariant domain; Relaxation limit

Indexed keywords

EID: 0036702873     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. A. Arnold, P. Markowich, G. Toscani and A. Unterreiter, On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations, Comm. Partial Differential Equations 26(1-2) (2001), 43-100.
2. A. Arnold, P. Markowich, G. Toscani and A. Unterreiter, On Csiszár-Kullback inequalities, Monatsh. Math. 131(3) (2000), 235-253.
3. F. Berthelin and F. Bouchut, Solution with finite energy to a BGK system relaxing to isentropic gas dynamics, Ann. Fac. Sci. Toulouse 9 (2000), 605-630.
4. F. Bouchut, Construction of BGK models with a family of kinetic entropies for a given system of conservation laws, J. Statist. Phys. 95 (1999), 113-170.
5. F. Bouchut, Renormalized solutions to the Vlasov equation with coefficients of bounded variation, Arch. Rational Mech. Anal. 157 (2001), 75-90.
6. Y. Brenier and L. Corrias, A kinetic formulation for multi-branch entropy solutions of scalar conservation laws, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998), 169-190.
7. G.Q. Chen, C.D. Levermore and T.-P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math. 47 (1994), 787-830.
8. R.J. DiPerna, Convergence of the viscosity method for isentropic gas dynamics, Comm. Math. Phys. 91 (1983), 1-30.
9. P.-L. Lions, B. Perthame and P.E. Souganidis, 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.
10. P.-L. Lions, B. Perthame and E. Tadmor, Kinetic formulation of the isentropic gas dynamics and p-systems, Comm. Math. Phys. 163 (1994), 415-431.
11. R. Natalini, A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws, J. Differential Equations 148 (1998), 292-317.
12. B. Perthame and E. Tadmor, A kinetic equation with kinetic entropy functions for scalar conservation laws, Comm. Math. Phys. 136 (1991), 501-517.
13. B. Perthame and A.E. Tzavaras. Kinetic formulation for systems of two conservation laws and elastodynamics, Arch. Rational Mech. Anal. 155 (2000), 1-48.
14. D. Serre, Relaxation semi-linéaire et cinétique des systèmes de lois de conservation, Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000), 169-192.
15. A.E. Tzavaras, Materials with internal variables and relaxation to conservation laws, Arch. Rational Mech. Anal. 146 (1999), 129-155.
16. A. Vasseur, Kinetic semidiscretization of scalar conservation laws and convergence by using averaging lemmas, SIAM J. Numer. Anal. 36 (1999), 465-474.
17. A. Vasseur, 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.