A kinetic formulation for multi-branch entropy solutions of scalar conservation laws

Y. Brenier; L. Corrias

Annales de l'I.H.P. Analyse non linéaire (1998)

  • Volume: 15, Issue: 2, page 169-190
  • ISSN: 0294-1449

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Brenier, Y., and Corrias, L.. "A kinetic formulation for multi-branch entropy solutions of scalar conservation laws." Annales de l'I.H.P. Analyse non linéaire 15.2 (1998): 169-190. <http://eudml.org/doc/78435>.

@article{Brenier1998,
author = {Brenier, Y., Corrias, L.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {entropy multivalued solutions; inviscid Burgers equation; moment equations},
language = {eng},
number = {2},
pages = {169-190},
publisher = {Gauthier-Villars},
title = {A kinetic formulation for multi-branch entropy solutions of scalar conservation laws},
url = {http://eudml.org/doc/78435},
volume = {15},
year = {1998},
}

TY - JOUR
AU - Brenier, Y.
AU - Corrias, L.
TI - A kinetic formulation for multi-branch entropy solutions of scalar conservation laws
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1998
PB - Gauthier-Villars
VL - 15
IS - 2
SP - 169
EP - 190
LA - eng
KW - entropy multivalued solutions; inviscid Burgers equation; moment equations
UR - http://eudml.org/doc/78435
ER -

References

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  2. [B2] Y. Brenier, Averaged Multivalued Solution for Scalar Conservation Laws, SIAM J. Numer. Anal., Vol. 21, 1984, pp. 1013-1037. Zbl0565.65054MR765504
  3. [Br] H. Brezis, Analyse fonctionnelle, Masson, 1987. Zbl0511.46001MR697382
  4. [C] S. Cordier, PHD dissertation, Ecole Polytechnique, 1994. 
  5. [DLM] R.J. Diperma, P.-L. Lions and Y. Meyer, Lp Regularity of Velocity Averages, Ann. Inst. Henri Poincaré, Vol. 8. 1991, pp. 271-287. Zbl0763.35014MR1127927
  6. [DM] L. Desvillettes and S. Mischler, About the Splitting Algorithm for Boltzmann and BGK Equations, preprint. Zbl0876.35088
  7. [EFO] B. Engquist, E. Fatemi and S. Osher, Numerical Solution of the High Frequency Asymptotic Expansion for Hyperbolic Equation, proc. ACES Conference, Applied Computational Electromagnetism, ACES, 1994, pp. 32-44. 
  8. [FF] A. Forestier and Ph. Le Floch, Multivalued Solutions to Some Non-Linear and Non-Strictly Hyperbolic Systems, Japan J. Ind. Appl. Math., Vol. 9, 1992, pp. 1-23. Zbl0768.35058MR1153771
  9. [G] H. Grad, On the Kinetic Theory of Rarefied Gases, Coom. Pure and Appl. Math., Vol. 2, 1949, pp. 331-404. Zbl0037.13104MR33674
  10. [GLPS] F. Golse, P.-L. Lions, B. Perthame, R. Sentis, Regularity of the moments of the solution of a transport equation, J. Funct. Anal., Vol. 76, 1988, pp. 110-125. Zbl0652.47031MR923047
  11. [GM] Y. Giga and T. Miyakawa, A Kinetic Construction of Global Solutions of First Order Quasilinear Equations, Duke Math. J., Vol. 50, 1983, pp. 505-515. Zbl0519.35053MR705037
  12. [KN] M.G. Krein and A.A. Nudelman, The Markov moment problem, AMS, Providence, 1977. 
  13. [L] D. Levermore, Moment Closure of the Boltzmann Equations, preprint 1994. 
  14. [LPT1] P.-L. Lions, B. Perthame and E. Tadmor, A Kinetic Formulation of Multidimensional Scalar Conservation Laws and Related Equations, J. A.M.S., Vol. 7, 1994, pp. 169-191. Zbl0820.35094MR1201239
  15. [LPT2] P.-L. Lions, B. Perthame and E. Tadmor, Kinetic Formulation of the Isentropic Gas Dynamics and p-Systems, Comm. Math. Phys., Vol. 163, 1994, pp. 415-431. Zbl0799.35151MR1284790
  16. [TS] J. Van Trier and W. Symes, Upwind Finite Difference Calculations of Travel Times, Geophysics, Vol. 56, 1991, pp. 812-821. 

Citations in EuDML Documents

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  1. Jean-David Benamou, Philippe Hoch, GO++ : a modular lagrangian/eulerian software for Hamilton Jacobi equations of geometric optics type
  2. Jean-David Benamou, Philippe Hoch, GO++: A modular Lagrangian/Eulerian software for Hamilton Jacobi equations of geometric optics type
  3. Olof Runborg, Some new results in multiphase geometrical optics
  4. Florent Berthelin, François Bouchut, Solution with finite energy to a BGK system relaxing to isentropic gas dynamics
  5. Olof Runborg, Some new results in multiphase geometrical optics
  6. Rémi Carles, Bijan Mohammadi, Numerical aspects of the nonlinear Schrödinger equation in the semiclassical limit in a supercritical regime
  7. Pierre-Emmanuel Jabin, Benoît Perthame, Kinetic methods for Line-energy Ginzburg–Landau models
  8. Rémi Carles, Bijan Mohammadi, Numerical aspects of the nonlinear Schrödinger equation in the semiclassical limit in a supercritical regime
  9. Benoît Perthame, Un cas limite de lemmes de compacité en moyenne motivé par la formulation cinétique de systèmes hyperboliques
  10. Pierre-Emmanuel Jabin, Benoît Perthame, Regularity in kinetic formulations via averaging lemmas

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