Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds

Matania Ben-Artzi; Philippe G. Le Floch

Annales de l'I.H.P. Analyse non linéaire (2007)

  • Volume: 24, Issue: 6, page 989-1008
  • ISSN: 0294-1449

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Ben-Artzi, Matania, and Le Floch, Philippe G.. "Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds." Annales de l'I.H.P. Analyse non linéaire 24.6 (2007): 989-1008. <http://eudml.org/doc/78773>.

@article{Ben2007,
author = {Ben-Artzi, Matania, Le Floch, Philippe G.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Riemannian manifold; Lorentzian; measure-valued solution; entropy; shock wave; vanishing diffusion method; finite volume method},
language = {eng},
number = {6},
pages = {989-1008},
publisher = {Elsevier},
title = {Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds},
url = {http://eudml.org/doc/78773},
volume = {24},
year = {2007},
}

TY - JOUR
AU - Ben-Artzi, Matania
AU - Le Floch, Philippe G.
TI - Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2007
PB - Elsevier
VL - 24
IS - 6
SP - 989
EP - 1008
LA - eng
KW - Riemannian manifold; Lorentzian; measure-valued solution; entropy; shock wave; vanishing diffusion method; finite volume method
UR - http://eudml.org/doc/78773
ER -

References

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  1. [1] Amorim P., Ben-Artzi M., LeFloch P.G., Hyperbolic conservation laws on manifolds. Total variation estimates and the finite volume method, Methods Appl. Anal.12 (2005) 291-324. Zbl1114.35121MR2254012
  2. [2] Dafermos C.M., Hyperbolic Conservation Laws in Continuum Physics, Grundlehren Math. Wiss., vol. 325, Springer-Verlag, 2000. Zbl0940.35002MR1763936
  3. [3] DiPerna R.J., Measure-valued solutions to conservation laws, Arch. Rational Mech. Anal.88 (1985) 223-270. Zbl0616.35055MR775191
  4. [4] Federer H., Geometric Measure Theory, Springer-Verlag, New York, 1969. Zbl0176.00801MR257325
  5. [5] Hörmander L., Nonlinear Hyperbolic Differential Equations, Math. Appl., vol. 26, Springer-Verlag, 1997. Zbl0881.35001MR1466700
  6. [6] Kruzkov S., First-order quasilinear equations with several space variables, English transl. in, Math. USSR-Sb.10 (1970) 217-243. Zbl0215.16203
  7. [7] Lax P.D., Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, Regional Conf. Series in Appl. Math., vol. 11, SIAM, Philadelphia, 1973. Zbl0268.35062MR350216
  8. [8] LeFloch P.G., Explicit formula for scalar conservation laws with boundary condition, Math. Methods Appl. Sci.10 (1988) 265-287. Zbl0679.35065MR949657
  9. [9] LeFloch P.G., Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves, Lectures in Mathematics, ETH Zürich, Birkhäuser, 2002. Zbl1019.35001MR1927887
  10. [10] LeFloch P.G., Nedelec J.-C., Explicit formula for weighted scalar non-linear conservation laws, Trans. Amer. Math. Soc.308 (1988) 667-683. Zbl0674.35058MR951622
  11. [11] Spivak M., A Comprehensive Introduction to Differential Geometry, vol. 4, Publish or Perish Inc., Houston, 1979. 
  12. [12] Volpert A.I., The space BV and quasi-linear equations, Mat. USSR-Sb.2 (1967) 225-267. 

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