The Flow Associated to Weakly Differentiable Vector Fields: Recent Results and Open Problems, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat, vol.10, issue.8, pp.1-25, 2007. ,
DOI : 10.1007/978-1-4419-9554-4_7
L1-Theory of Scalar Conservation Law with Continuous Flux Function, Journal of Functional Analysis, vol.171, issue.1, pp.1-15, 2000. ,
DOI : 10.1006/jfan.1999.3445
Renormalized Entropy Solutions for Quasi-linear Anisotropic Degenerate Parabolic Equations, SIAM Journal on Mathematical Analysis, vol.36, issue.2, pp.405-422, 2004. ,
DOI : 10.1137/S0036141003428937
Conservation laws with continuous flux functions, NoDEA Nonlin. Diff. Eq. Appl, vol.3, issue.4, pp.395-419, 1996. ,
Renormalized entropy solutions of scalar conservation laws, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.29, issue.42, pp.313-327, 2000. ,
Vanishing viscosity solutions of nonlinear hyperbolic systems, Annals of Mathematics, vol.161, issue.1, pp.223-342, 2005. ,
DOI : 10.4007/annals.2005.161.223
Kruzhkov's estimates for scalar conservation laws revisited, Trans. Amer. Math. Soc, vol.350, pp.7-2847, 1998. ,
R??solution d'??quations d'??volution quasilin??aires en dimension N d'espace ?? l'aide d'??quations lin??aires en dimension N + 1, Journal of Differential Equations, vol.50, issue.3, pp.3-375, 1983. ,
DOI : 10.1016/0022-0396(83)90067-0
L 2 formulation of multidimensional scalar conservation laws, to appear in Arch, Ration. Mech. Anal ,
Hyperbolic systems of conservation laws. The one-dimensional Cauchy problem, 2000. ,
Entropy Solutions for Nonlinear Degenerate Problems, Archive for Rational Mechanics and Analysis, vol.147, issue.4, pp.269-361, 1999. ,
DOI : 10.1007/s002050050152
Well-posedness for non-isotropic degenerate parabolic-hyperbolic equations, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.20, issue.4, pp.645-668, 2003. ,
DOI : 10.1016/S0294-1449(02)00014-8
Hyperbolic conservation laws in continuum physics, 2005. ,
Structure of Entropy Solutions for Multi-Dimensional Scalar Conservation Laws, Archive for Rational Mechanics and Analysis, vol.170, issue.2, pp.137-184, 2003. ,
DOI : 10.1007/s00205-003-0270-9
Partial differential equations, 1998. ,
Problems book on differential equations, 1976. ,
A kinetic construction of global solutions of first order quasilinear equations, Duke Math, J, vol.50, issue.2, pp.505-515, 1983. ,
Hyperbolic systems of conservation laws, 1991. ,
URL : https://hal.archives-ouvertes.fr/hal-00113734
On locally bounded generalized entropy solutions of the Cauchy problem for a first-order quasilinear equation, Proc. Steklov Inst. Math, pp.120-1331, 2002. ,
Front tracking for hyperbolic conservation laws, 2002. ,
The partial differential equation ut + uux = ??xx, Communications on Pure and Applied Mathematics, vol.3, issue.3, pp.201-230, 1950. ,
DOI : 10.1002/cpa.3160030302
Isentropic solutions of quasilinear equations of the first order, Sbornik: Mathematics, vol.197, issue.5, pp.5-99, 2006. ,
DOI : 10.1070/SM2006v197n05ABEH003776
Generalized solutions of the Cauchy problem in the large for first order nonlinear equations, Dokl. Akad. Nauk. SSSR English transl. in Soviet Math. Dokl, vol.187, issue.10, pp.29-32, 1969. ,
FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES, Mathematics of the USSR-Sbornik, vol.10, issue.2, pp.123-228, 1970. ,
DOI : 10.1070/SM1970v010n02ABEH002156
Nonlinear Partial Differential Equations (Lectures). Part II. First-order equations, 1970. ,
First-order conservative quasilinear laws with an infinite domain of dependence on the initial data, Dokl. Akad. Nauk SSSR English transl. in Soviet Math. Dokl, vol.314, issue.422, pp.1-79, 1990. ,
On the construction of discontinuous solutions of quasi-linear hyperbolic equations as limits of solutions of the corresponding parabolic equations when the " coefficient of viscosity " tends towards zero, Dokl. Akad. Nauk SSSR, vol.111, issue.2, pp.291-294, 1956. ,
Hyperbolic systems of conservation laws, II, Comm. Pure Appl. Math, vol.10, issue.1, pp.537-566, 1957. ,
DOI : 10.1090/cln/014/10
Weak solutions of nonlinear hyperbolic equations and their numerical computation, Communications on Pure and Applied Mathematics, vol.24, issue.1, pp.159-193, 1954. ,
DOI : 10.1002/cpa.3160070112
Hyperbolic partial differential equations, Courant Lect. Notes in Math, vol.14, 2006. ,
DOI : 10.1090/cln/014
Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves, Applied Mechanics Reviews, vol.56, issue.4, 2002. ,
DOI : 10.1115/1.1579455
A kinetic formulation of multidimensional scalar conservation laws and related equations, Journal of the American Mathematical Society, vol.7, issue.1, pp.169-191, 1994. ,
DOI : 10.1090/S0894-0347-1994-1201239-3
Weak and measure-valued solutions to evolutionary PDEs, 1996. ,
DOI : 10.1007/978-1-4899-6824-1
Discontinuous solutions of non-linear differential equations, Uspehi Mat. Nauk, pp.3-3, 1957. ,
Initial-boundary value problem for a scalar conservation law, C. R. Acad. Sci. Paris Sér. I Math, vol.322, pp.8-729, 1996. ,
Uniqueness of the solution of the Cauchy problem for a first-order quasilinear equation with an admissible strictly convex entropy, Mat. Zametki, pp.55-116, 1994. ,
On sequences of measure valued solutions for a first order quasilinear equation, Mat. Sb. English transl. in Russian Acad. Sci. Sb. Math, vol.185, issue.81, pp.87-1061, 1994. ,
Property of strong precompactness for bounded sets of measure valued solutions of a first-order quasilinear equation, Mat. Sb. English transl. in Sb. Math, vol.190, issue.190, pp.3-109, 1999. ,
On the theory of generalized entropy solutions of the Cauchy problem for a firstorder quasilinear equation in the class of locally integrable functions, Izvest. RAN Izvestiya: Mathematics, pp.91-1366, 2002. ,
On kinetic formulation of first-order hyperbolic quasilinear systems, Ukr. Math. Bull, vol.1, issue.4, pp.553-568, 2004. ,
? ? -Shock waves as a new type of solutions to systems of conservation laws, J. Diff. Eq, vol.228, pp.1-49, 2006. ,
On kinetic formulation of measure valued solutions for hyperbolic first-order quasilinear equations with several space variables, in: Analytical Approaches to Multidimensional Balance Laws, 2007. ,
Existence of strong traces for quasi-solutions of multidimensional conservation laws, J. Hyperbolic Differ. Equ, vol.4, issue.4, pp.729-770, 2007. ,
Kinetic formulation of conservation laws, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-01146188
Systems of conservation laws. 1. Hyperbolicity, entropies, shock waves. and Systems of conservation laws. 2. Geometric structures, oscillations, and initial-boundary value problems . Transl. from the 1996 French original, 1999. ,
URL : https://hal.archives-ouvertes.fr/ensl-01402415
Shock waves and reaction-diffusion equations, 1994. ,
Samarski? ?. On discontinuous solutions of a quasilinear equation of first order, Dokl. Akad. Nauk SSSR, vol.99, pp.1-27, 1954. ,
Strong Traces for Solutions of Multidimensional Scalar Conservation Laws, Archive for Rational Mechanics and Analysis, vol.160, issue.3, pp.181-193, 2001. ,
DOI : 10.1007/s002050100157