OPTIMAL ENTROPY SOLUTIONS FOR CONSERVATION LAWS WITH DISCONTINUOUS FLUX-FUNCTIONS, Journal of Hyperbolic Differential Equations, vol.02, issue.04, pp.783-837, 2005. ,
DOI : 10.1142/S0219891605000622
Lecture Notes on Optimal Transport Problems, Lecture Notes in Math, vol.1812, pp.1-52, 2003. ,
DOI : 10.1007/978-3-540-39189-0_1
Transport equation and Cauchy problem for BV vector fields and applications, Journ??es ??quations aux d??riv??es partielles, vol.158, issue.2, pp.227-260, 2004. ,
DOI : 10.5802/jedp.1
URL : http://archive.numdam.org/article/JEDP_2004____A1_0.pdf
De Philippis, A nonautonomous chain rule in W 1,p and BV, Manuscripta Math, vol.140, pp.3-4, 2013. ,
Free Discontinuity Problems and Special Functions with Bounded Variation, p.185729249002, 2000. ,
DOI : 10.1007/978-3-0348-8974-2_2
A Theory of L 1-Dissipative Solvers for Scalar Conservation Laws with Discontinuous Flux, Archive for Rational Mechanics and Analysis, vol.2, issue.2, pp.27-86, 2011. ,
DOI : 10.1007/s00205-010-0389-4
URL : https://hal.archives-ouvertes.fr/hal-00475840
On vanishing viscosity approximation of conservation laws with discontinuous flux, Netw. Heterog. Media, vol.5, issue.3, pp.617-633, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00438203
Entropy conditions for scalar conservation laws with discontinuous flux revisited, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.32, issue.6, pp.1307-1335, 2015. ,
DOI : 10.1016/j.anihpc.2014.08.002
URL : https://hal.archives-ouvertes.fr/hal-00978482
Uniqueness for scalar conservation laws with discontinuous flux via adapted entropies, Proc. Roy. Soc. Edinburgh Sect. A, vol.135, issue.2, pp.253-265, 2005. ,
Conservation Laws with Time Dependent Discontinuous Coefficients, SIAM Journal on Mathematical Analysis, vol.36, issue.4, pp.1293-1309, 2005. ,
DOI : 10.1137/S0036141002420005
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.229.813
Kinetic Formulation and Uniqueness for Scalar Conservation Laws with Discontinuous Flux, Communications in Partial Differential Equations, vol.73, issue.4, pp.694-726, 2015. ,
DOI : 10.1016/S0021-7824(99)80003-8
Notes on hyperbolic systems of conservation laws and transport equations, Handbook of differential equations: evolutionary equations, Handb. Differ. Equ, vol.III, pp.277-382, 2007. ,
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
A UNIQUENESS CONDITION FOR NONLINEAR CONVECTION-DIFFUSION EQUATIONS WITH DISCONTINUOUS COEFFICIENTS, Journal of Hyperbolic Differential Equations, vol.06, issue.01, pp.127-159, 2009. ,
DOI : 10.1142/S0219891609001794
Ordinary differential equations, transport theory and Sobolev spaces, Inventiones Mathematicae, vol.307, issue.3, pp.511-547, 1989. ,
DOI : 10.1007/BF01393835
Conservation laws with discontinuous flux, Networks and Heterogeneous Media, vol.2, issue.1, pp.159-179, 2007. ,
DOI : 10.3934/nhm.2007.2.159
Towers, L 1 stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients, Skr. K. Nor. Vidensk. Selsk, issue.3, pp.1-49, 2003. ,
FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES, Mathematics of the USSR-Sbornik, vol.10, issue.2, pp.228-255, 1970. ,
DOI : 10.1070/SM1970v010n02ABEH002156
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
New entropy conditions for scalar conservation laws with discontinuous flux, Discrete Contin, Dyn. Syst, vol.30, issue.4, pp.1191-1210, 2011. ,
Proper entropy conditions for scalar conservation laws with discontinuous flux, 2012. ,
DOI : 10.3934/dcds.2011.30.1191
URL : http://arxiv.org/abs/1011.4236
Panov, Existence of strong traces for quasi-solutions of multidimensional conservation laws, J. Hyperbolic Differ. Equ, vol.4, issue.4, pp.729-770, 2007. ,
Existence and strong pre-compactness properties for entropy solutions of a first-order quasilinear equation with discontinuous flux, Arch. Ration. Mech. Anal, vol.195, issue.2, pp.643-673, 2010. ,
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
Moro 2 ? I-00185 Roma (Italy) E-mail address: crasta@mat.uniroma1.it Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Univ. di Roma I, Via A. Scarpa 10 ? I-00185 Roma (Italy) E-mail address: virginia.decicco@sbai.uniroma1, pp.190-8057 ,