Renormalized entropy solutions of scalar conservation laws

Philippe Bénilan; Jose Carrillo; Petra Wittbold

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2000)

  • Volume: 29, Issue: 2, page 313-327
  • ISSN: 0391-173X

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Bénilan, Philippe, Carrillo, Jose, and Wittbold, Petra. "Renormalized entropy solutions of scalar conservation laws." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 29.2 (2000): 313-327. <http://eudml.org/doc/84408>.

@article{Bénilan2000,
author = {Bénilan, Philippe, Carrillo, Jose, Wittbold, Petra},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {nonlinear semigroup theory; Cauchy problem; mild solutions; renormalized entropy sub- and super-solutions},
language = {eng},
number = {2},
pages = {313-327},
publisher = {Scuola normale superiore},
title = {Renormalized entropy solutions of scalar conservation laws},
url = {http://eudml.org/doc/84408},
volume = {29},
year = {2000},
}

TY - JOUR
AU - Bénilan, Philippe
AU - Carrillo, Jose
AU - Wittbold, Petra
TI - Renormalized entropy solutions of scalar conservation laws
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2000
PB - Scuola normale superiore
VL - 29
IS - 2
SP - 313
EP - 327
LA - eng
KW - nonlinear semigroup theory; Cauchy problem; mild solutions; renormalized entropy sub- and super-solutions
UR - http://eudml.org/doc/84408
ER -

References

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  1. [1] B. Andreianov - PH. Bénilan - S.N. Kruzhkov, L1 -theory of scalar conservation law with continuous flux function, to appear in J. Funct. Anal. Zbl0944.35048MR1742856
  2. [2] L. Barthélemy, Problème d'obstacle pour une équation quasi-linéaire du premier ordre, Ann. Fac. Sci. Toulouse Math. (6) 9 (1988),137-159. Zbl0631.47038MR1425004
  3. [3] PH. Bénilan - L. Boccardo - TH. Gallouët - R. Gariepy - M. Pierre - J.-L. Vazquez, An L 1-theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 22 (1995), 241-273. Zbl0866.35037MR1354907
  4. [4] PH. Bénilan, "Equations d'évolution dans un espace de Banach quelconque et applications ", Thèse d'Etat, Orsay, 1972. 
  5. [5] PH. Bénilan - S.N. Kruzhkov, Conservation laws with continuous flux functions, Nonlinear Differential Equations Appl.3 (1996), 395-419. Zbl0961.35088MR1418588
  6. [6] PH. Bénilan - A. Pazy - M.G. Crandall, "Nonlinear Evolution Equations in Banach Spaces", book to appear. Zbl0249.34049
  7. [7] D. Blanchard - F. Murat, Renormalised solutions of nonlinear parabolic problems with L1-data: existence and uniqueness, Proc. Royal Soc. Edinburgh Sect.A127 (1997), 1137-1152. Zbl0895.35050MR1489429
  8. [8] D. Blanchard - H. Redwane, Solutions rénormalisées d'équations paraboliques à deux nonlinéarités, C.R. Acad. Sci. Paris Sér. I Math.319 (1994), 831-835. Zbl0810.35038MR1300952
  9. [9] J. Carrillo - P. Wittbold, Scalar conservation laws in L 1 with boundary conditions, in preparation. Zbl1026.35069
  10. [10] J. Carrillo - P. Wittbold, Renormalized entropy solutions of quasilinear equations in divergence form, in preparation. Zbl1026.35069
  11. [11] M.G. Crandall, The semigroup approach to first order quasilinear equations in several space variables, Israel J. Math.12 (1972), 108-122. Zbl0246.35018MR316925
  12. [12] M.G. Crandall - T. Liggett, Generation of semi-groups of nonlinear transformations in general Banach spaces, Amer. J. Math.93 (1971), 265-298. Zbl0226.47038MR287357
  13. [13] G. Dal Maso - F. Murat - L. Orsina - A. Prignet, Renormalized solutions of elliptic equations, to appear in Ann. Sc. Norm. Sup. di Pisa. Zbl0887.35057
  14. [14] G. Dal Maso - F. Murat - L. Orsina - A. Prignet, Definition and existence of renormalized solutions of elliptic equations with general measure data, C. R. Acad. Sci. Paris Sér. I Math.325 (1997), 481-486. Zbl0887.35057MR1692311
  15. [15] R.J. Di Perna - P.L. Lions, On the Cauchy problem for Boltzmann equations: global existence and weak stability, Ann. of Math.130 (1989), 321-366. Zbl0698.45010MR1014927
  16. [16] A. Yu. Goritsky - E. Yu. Panov, Example of Nonuniqueness of Entropy Solutions in the Class of Locally Bounded Functions, Russian Journal of Math. Physics6, No. 4 (1999), 492-494. Zbl1059.35503MR1815366
  17. [17] S.N. Kruzhkov, Generalized solutions of the Cauchy problem in the large for first-order nonlinear equations, Dokl. Akad. Nauk SSSR187 (1969), 29-32; English tr. in Soviet. Math. Dokl.10 (1969), 785-788. Zbl0202.37701MR249805
  18. [18] S.N. Kruzhkov, First-order quasilinear equations in several independent variables, Mat. Sbornik81 (1970), 228-255; English tr. in Math. USSR Sb.10 (1970), 217-243. Zbl0215.16203MR267257
  19. [19] F. Murat, Soluciones renormalizadas de EDP elipticas no lineales, Publ. Laboratoire d' Analyse Numérique, Univ. Paris6, R 93023 (1993). 

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