Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 6, pp. 989-1008. 
@article{AIHPC_2007__24_6_989_0,
     author = {Ben-Artzi, Matania and Le Floch, Philippe G.},
     title = {Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {989--1008},
     publisher = {Elsevier},
     volume = {24},
     number = {6},
     year = {2007},
     doi = {10.1016/j.anihpc.2006.10.004},
     mrnumber = {2371116},
     zbl = {1138.35055},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2006.10.004/}
}
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Ben-Artzi, Matania; Le Floch, Philippe G. Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 6, pp. 989-1008. doi : 10.1016/j.anihpc.2006.10.004. http://archive.numdam.org/articles/10.1016/j.anihpc.2006.10.004/

[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. | MR | Zbl

[2] Dafermos C.M., Hyperbolic Conservation Laws in Continuum Physics, Grundlehren Math. Wiss., vol. 325, Springer-Verlag, 2000. | MR | Zbl

[3] Diperna R.J., Measure-valued solutions to conservation laws, Arch. Rational Mech. Anal. 88 (1985) 223-270. | MR | Zbl

[4] Federer H., Geometric Measure Theory, Springer-Verlag, New York, 1969. | MR | Zbl

[5] Hörmander L., Nonlinear Hyperbolic Differential Equations, Math. Appl., vol. 26, Springer-Verlag, 1997. | MR | Zbl

[6] Kruzkov S., First-order quasilinear equations with several space variables, English transl. in, Math. USSR-Sb. 10 (1970) 217-243. | Zbl

[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. | MR | Zbl

[8] Lefloch P.G., Explicit formula for scalar conservation laws with boundary condition, Math. Methods Appl. Sci. 10 (1988) 265-287. | MR | Zbl

[9] Lefloch P.G., Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves, Lectures in Mathematics, ETH Zürich, Birkhäuser, 2002. | MR | Zbl

[10] Lefloch P.G., Nedelec J.-C., Explicit formula for weighted scalar non-linear conservation laws, Trans. Amer. Math. Soc. 308 (1988) 667-683. | MR | Zbl

[11] Spivak M., A Comprehensive Introduction to Differential Geometry, vol. 4, Publish or Perish Inc., Houston, 1979.

[12] Volpert A.I., The space BV and quasi-linear equations, Mat. USSR-Sb. 2 (1967) 225-267.

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