Kinetic formulation for heterogeneous scalar conservation laws

Anne-Laure Dalibard

Annales de l'I.H.P. Analyse non linéaire (2006)

  • Volume: 23, Issue: 4, page 475-498
  • ISSN: 0294-1449

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Dalibard, Anne-Laure. "Kinetic formulation for heterogeneous scalar conservation laws." Annales de l'I.H.P. Analyse non linéaire 23.4 (2006): 475-498. <http://eudml.org/doc/78699>.

@article{Dalibard2006,
author = {Dalibard, Anne-Laure},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {entropy solutions; existence; uniqueness; weak solutions},
language = {eng},
number = {4},
pages = {475-498},
publisher = {Elsevier},
title = {Kinetic formulation for heterogeneous scalar conservation laws},
url = {http://eudml.org/doc/78699},
volume = {23},
year = {2006},
}

TY - JOUR
AU - Dalibard, Anne-Laure
TI - Kinetic formulation for heterogeneous scalar conservation laws
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2006
PB - Elsevier
VL - 23
IS - 4
SP - 475
EP - 498
LA - eng
KW - entropy solutions; existence; uniqueness; weak solutions
UR - http://eudml.org/doc/78699
ER -

References

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  1. [1] Dafermos C.M., Hyperbolic Conservation Laws in Continuum Physics, Grundlehren Math. Wiss., vol. 325, Springer-Verlag, Berlin, 1999. Zbl0940.35002MR2169977
  2. [2] DiPerna R., Measure-valued solutions to conservation laws, Arch. Rational Mech. Anal.88 (1985) 223-270. Zbl0616.35055MR775191
  3. [3] Kruzkhov S.N., Generalized solutions of the Cauchy problem in the large for nonlinear equations of first order, Soviet Math. Dokl.10 (1969). Zbl0202.37701
  4. [4] Kruzkhov S.N., First order quasilinear equations in several independent variables, Math. USSR-Sb.10 (1970) 217-243. Zbl0215.16203
  5. [5] Lions P.-L., Perthame B., Tadmor E., Formulation cinétique des lois de conservation scalaires multidimensionnelles, C. R. Acad. Sci. Paris, Sér. I312 (1991) 97-102. Zbl0729.49007MR1086510
  6. [6] Lions P.-L., Perthame B., Tadmor E., A kinetic formulation of multidimensional conservation laws and related equations, J. Amer. Math. Soc.7 (1994) 169-191. Zbl0820.35094MR1201239
  7. [7] Perthame B., Kinetic Formulation of Conservation Laws, Oxford Lecture Series in Math. Appl., vol. 21, Oxford University Press, New York, 2002. Zbl1030.35002MR2064166
  8. [8] Perthame B., Uniqueness and error estimates in first order quasilinear conservation laws via the kinetic entropy defect measure, J. Math. Pures Appl.77 (1998) 1055-1064. Zbl0919.35088MR1661021
  9. [9] Perthame B., Tadmor E., A kinetic equation with kinetic entropy functions for scalar conservation laws, Comm. Math. Phys.136 (1991) 501-517. Zbl0729.76070MR1099693
  10. [10] Serre D., Systèmes de lois de conservation I et II, Diderot Editeur, Arts et Sciences, 1996. MR1459988
  11. [11] Szepessy A., An existence result for scalar conservation laws using measure valued solutions, Comm. Partial Differential Equations14 (1989) 1329-1349. Zbl0704.35022MR1022989

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