Mathematical analysis of a scalar multidimensional conservation law with discontinuous flux

Julien Jimenez1
1Université de Pau et des Pays de l’Adour, Laboratoire de Mathématiques Appliquées - UMR 5142 CNRS, BP 1155, 64013, PAU Cedex, France

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Adimurthi J., Jaffre G.D., Veerappa Gowda: Godunov-type methods for conservation laws with a flux function discontinuous in space. SIAM J. Numer. Anal. 42, 179–208 (2004)

Adimurthi S., Mishra G.D., Veerappa Gowda: Optimal entropy solutions for conservation laws with discontinuous flux function. J. Hyperbolic Differ. Equ. 2, 783–837 (2005)

Adimurthi S., Mishra G.D., Veerappa Gowda: Existence and stability of entropy solutions for a conservation law with discontinuous non-convex fluxes. Netw. Heterog. Media 2, 127–157 (2007)

Audusse E., Perthame B.: Uniqueness for scalar conservation laws with discontinuous flux via adapted entropies. Proc. Roy. Soc. Edinburgh Sect. A 135, 253–265 (2005)

Bachmann F.: Analysis of a scalar conservation law with a flux function with discontinuous coefficients. Advances in Differential equations 9(11–12), 1317–1338 (2004)

Bachmann F., Vovelle J.: Existence and uniqueness of entropy solution of scalar conservation laws with a flux function involving discontinuous coefficients. Comm. Partial Differential Equations 31, 371–395 (2006)

Bardos C., LeRoux A.Y, Nédélec J.C: First order quasilinear equations with boundary conditions. Comm. in partial differential equations 4, 1017–1034 (1979)

Bürger R., Karlsen K.H., Risebro N.H., Towers J.D.: Well-posedness in BV t and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units. Numer. Math. 97, 25–65 (2004)

Bürger R., Karlsen K.H., Towers J.D.: A model of continuous sedimentation of flocculated suspensions in clarifier-thickener units. SIAM J. Appl. Math. 65, 882–840 (2005)

Chen G.-Q., Frid H.: Divergence-Measure fields and hyperbolic conservation laws. Arch. Rational Mech. Anal. 147, 89–118 (1999)

G. Gagneux, M. Madaune-Tort : Analyse mathématique de modèles nonlinéaires de l’ingénierie pétrolière, Mathématiques et Applications 22, Springer-Verlag, Berlin, 1996.

Gimse T., Risebro N.H.: Solution of the Cauchy problem for a conservation law with a discontinuous flux function. SIAM J. Math. Anal. 23, 635–648 (1992)

J. Jimenez: Some Scalar Conservation Laws with Discontinuous Flux, Int. J. Evol. Equ. 2(3), 2007.

Karlsen K.H., Rascle M., Tadmor E.: On the existence and compactness of a two-dimensional resonant system of conservation law. Comm. Math. Sci. 5(2), 253–265 (2007)

K.H. Karlsen, N.H. Risebro, J.D. Towers: L 1 stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients, Skr. K. Nor. Vid. Selsk. 49 pp, 2003.

Karlsen K.H., Towers J.D.: Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux. Chin. Ann. Math. 25, 287–318 (2004)

Kruzkov S.N.: First-order quasilinear equations with several independent variables. Mat. Sb. 81, 228–255 (1970)

J. Màlex, J. Nečas, M. Rokyta, M. Růžička: Weak and mesure-valued solutions to evolutionary PDEs Applied Mathematics and Mathematical Computation 13, Chapman & Hall, London, 1996.

F. Otto: Initial-Boundary Value Problem for a Scalar Conservation Law, C.R. Acad. Sci. Paris 322, série I, 729–734, 1996.

Panov E.Yu.: Property of strong precompactness for bounded sets of measure valued solutions of a first-order quasilinear equation. Sbornik: Mathematics 190(3), 427–446 (1999)

Panov E.Yu.: Existence of strong traces for generalized solutions of multidimensional scalar conservation laws. J. Hyperbolic Differ. Equ. 2(4), 885–908 (2005)

Panov E.Yu.: Existence and strong precompactness properties for entropy solutions of a first-order quasilinear equation with discontinuous flux. Arch. Ration. Mech. Anal. 195(2), 643–673 (2009)

Seguin N., Vovelle J.: Analysis and approximation of a scalar conservation law with a flux fonction with discontinuous coefficients. Math. Models Methods Appl. Sci. 13(2), 221–257 (2003)

Towers J.D.: Convergence of a difference scheme for conservation laws with a discontinuous flux. SIAM J. Numer. Anal. 38, 681–698 (2000)

Vasseur A.: Strong traces for solutions of multidimensional scalar conservation laws. Arch. Rational Mech. Anal. 160(3), 181–193 (2001)