Solution with finite energy to a BGK system relaxing to isentropic gas dynamics

Florent Berthelin; François Bouchut

Annales de la Faculté des sciences de Toulouse : Mathématiques (2000)

  • Volume: 9, Issue: 4, page 605-630
  • ISSN: 0240-2963

How to cite

top

Berthelin, Florent, and Bouchut, François. "Solution with finite energy to a BGK system relaxing to isentropic gas dynamics." Annales de la Faculté des sciences de Toulouse : Mathématiques 9.4 (2000): 605-630. <http://eudml.org/doc/73529>.

@article{Berthelin2000,
author = {Berthelin, Florent, Bouchut, François},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {gas dynamics with relaxation; entropy solution; kinetic formulation; existence},
language = {eng},
number = {4},
pages = {605-630},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Solution with finite energy to a BGK system relaxing to isentropic gas dynamics},
url = {http://eudml.org/doc/73529},
volume = {9},
year = {2000},
}

TY - JOUR
AU - Berthelin, Florent
AU - Bouchut, François
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
PB - UNIVERSITE PAUL SABATIER
VL - 9
IS - 4
SP - 605
EP - 630
LA - eng
KW - gas dynamics with relaxation; entropy solution; kinetic formulation; existence
UR - http://eudml.org/doc/73529
ER -

References

top
  1. [1] Aregba-Driollet ( D.), Natalini ( R.). — Discrete kinetic schemes for multidimensional systems of conservation laws, SIAM J. Numer. Anal.37 (2000), 1973-2004. Zbl0964.65096MR1766856
  2. [2] Berthelin ( F.), Bouchut ( F.). - Kinetic invariant domains and relaxation limit from a BGK model to isentropic gas dynamics, to appear in Asymptotic Analysis. Zbl1032.76064MR1938602
  3. [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. Zbl0957.82028MR1705583
  4. [4] Brenier ( Y.). — Averaged multivalued solutions for scalar conservation laws, SIAM J. Numer. Anal.21 (1984), 1013-1037. Zbl0565.65054MR765504
  5. [5] Brenier ( Y.), Corrias ( L.). — A kinetic formulation for multi-branch entropy solutions of scalar conservation laws, Ann. Inst. H. Poincaré Anal. Non Linéaire15 (1998), 169-190. Zbl0893.35068MR1614638
  6. [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. Zbl0806.35112MR1280989
  7. [7] Diperna ( R.J.). — Convergence of the viscosity method for isentropic gas dynamics, Comm. Math. Phys.91 (1983), 1-30. Zbl0533.76071MR719807
  8. [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. Zbl0652.47031MR923047
  9. [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. Zbl0826.65078MR1322811
  10. [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. Zbl0853.76077MR1383202
  11. [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. Zbl0820.35094MR1201239
  12. [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. Zbl0799.35151MR1284790
  13. [13] Natalini ( R.). — A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws, J. Diff. Eq.148 (1998), 292-317. Zbl0911.35073MR1643175
  14. [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. Zbl0940.35127
  15. [15] Perthame ( B.). — Global existence to the BGK model of Boltzmann equation, J. Diff. Eq.82 (1989), 191-205. Zbl0694.35134MR1023307
  16. [16] Perthame ( B.), Pulvirenti ( M.). - Weighted L∞ bounds and uniqueness for the Boltzmann BGK model, Arch. Rational Mech. Anal.125 (1993), 289-295. Zbl0786.76072MR1245074
  17. [17] Perthame ( B.), Tadmor ( E.). — A kinetic equation with kinetic entropy functions for scalar conservation laws, Comm. Math. Phys.136 (1991), 501-517. Zbl0729.76070MR1099693
  18. [18] Serre ( D.). — Relaxation semi-linéaire et cinétique des systèmes de lois de conservation, Ann. Inst. H. Poincaré Anal. non linéaire17 (2000), 169-192. Zbl0963.35117MR1753092

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.