Asymptotic time-behavior for weighted scalar conservation laws

Philippe Le Floch; J. C. Nedelec

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1988)

  • Volume: 22, Issue: 3, page 469-475
  • ISSN: 0764-583X

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Le Floch, Philippe, and Nedelec, J. C.. "Asymptotic time-behavior for weighted scalar conservation laws." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 22.3 (1988): 469-475. <http://eudml.org/doc/193538>.

@article{LeFloch1988,
author = {Le Floch, Philippe, Nedelec, J. C.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {entropy weak solution},
language = {eng},
number = {3},
pages = {469-475},
publisher = {Dunod},
title = {Asymptotic time-behavior for weighted scalar conservation laws},
url = {http://eudml.org/doc/193538},
volume = {22},
year = {1988},
}

TY - JOUR
AU - Le Floch, Philippe
AU - Nedelec, J. C.
TI - Asymptotic time-behavior for weighted scalar conservation laws
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1988
PB - Dunod
VL - 22
IS - 3
SP - 469
EP - 475
LA - eng
KW - entropy weak solution
UR - http://eudml.org/doc/193538
ER -

References

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  1. [1] E. D. CONWAY, The formation and decay of shocks for a conservation law in several dimensions, Arch. Rat. M.A. 64 (1977) pp. 47-57. Zbl0352.35029MR427850
  2. [2] C. M . DAFERMOS, Characteristics in hyperbolic conservation law, in « Nonlinear analysis and mechanics : Heriot-Watt Symposium vol. 1 », Knops Editor (1983). Zbl0373.35048
  3. [3]. F. DUBOIS, Ph. LE FLOCH, Boundary conditions for nonlinear hyperbolic systems of conservation laws, Internal Report (1987), École Polytechnique ; J. of Diff. Eq., Vol. 71, No 1, jan. 1988, pp. 93-122. Zbl0649.35057MR922200
  4. [4] F. DUBOIS, Ph. LE FLOCH, Condition à la limite pour un système de lois de conservation, Note Compt. Rend. Acad. Sc. Paris, t. 304, Série I, n° 3, pp. 75-78 (1987). Zbl0634.35046MR878830
  5. [5] B. KEYFITZ, Solutions with shocks, an example of Ll -contractive semi-group, Comm. Pure Appl. Math., 24 (1971) pp. 125-132. Zbl0206.10401MR271545
  6. [6] S. N. KRUSKOV, First order quasi-linear equations in several independant variables, Math. USSR Sb., 10 1970) n° 2, pp. 217-243. 
  7. [7] P. D. LAX, Conservation laws and the mathematical theory of shock waves, CBMS Ser. Appl. Math, vol. 11, SIAM, Philadelphia (1973). Zbl0268.35062MR350216
  8. [8] Ph. LE FLOCH, Explicit formula for scalar conservation laws with boundary conditions, to appear in Math. Meth. in Appl. Sc. (1988) vol. 10. Zbl0679.35065MR949657
  9. [9] Ph. LE FLOCH, Generalized Riemann problem and boundary conditions for systems of conservation laws, Thesis (1987) École Polytechnique (France). 
  10. [10] Ph. LE FLOCH, J. C. NEDELEC, Explicit formula for weighted scalar conservation laws, Internal Report n° 144 (janv. 1986) of École Polytechnique ; accepted for publication to Transactions of A.M.S. 
  11. [11] Ph. LE FLOCH, J. C. NEDELEC, Lois de conservation scalaires avec poids, Note Compt. Rend. Acad. Sc. Paris, t. 301, Série I, n° 17, pp. 1301-1304 (1985). Zbl0612.35084MR822833
  12. [12] Ph. LE FLOCH, P. A. RAVIART, Un développement asymptotique pour le problème de Riemann généralisé, Compt. Rend. Acad. Se. Paris, t. 304, Série I, n° 4, pp. 119-122 (1987) and Ann. Henri Poincaré, Analyse non linéaire. Zbl0619.35074MR890629
  13. [13] T. P. LIU, M. PIERRE, Source-solutions and asymptotic behavior in conservation laws, J. of Diff. Eq. 51, 419-441 (1984). Zbl0545.35057MR735207
  14. [14] O. A. OLEINIK, Discontinuous solutions of nonlinear differential equations, A.M.S. Transal., Ser. 2, 26, pp. 95-172 (1963). 
  15. [15] M.E. SCHONBEK, Existence of solutions to singular conservation laws, Siam J. Math. Anal., vol. 15, n° 6 (nov. 1984). Zbl0567.35060MR762969
  16. [16] J. A. SMOLLER, Reaction-Diffusion Equations and Shock Waves, Springer, Verlag 258 (1983). Zbl0508.35002
  17. [17] G.B. WHITHAM, Linear and Non linear Waves, Wiley Interscience, New York (1974). Zbl0373.76001MR483954

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