R. Adimurthi, S. S. Dutta, G. D. Ghoshal, and . Veerappa-gowda, Existence and nonexistence of TV bounds for scalar conservation laws with discontinuous flux, Comm. Pure Appl. Math, vol.64, issue.1, pp.84-115, 2011.

S. S. Adimurthi, G. D. Ghoshal, and . Veerappa-gowda, Structure of entropy solutions to scalar conservation laws with strictly convex flux, J. Hyperbolic Differ. Equ, vol.4, pp.571-611, 2012.

S. S. Adimurthi, G. D. Ghoshal, and . Veerappa-gowda, Exact controllability of scalar conservation law with strict convex flux, Math. Control Relat. Fields, vol.4, issue.4, pp.401-449, 2014.

S. S. Adimurthi, G. D. Ghoshal, and . Veerappa-gowda, Finer regularity of an entropy solution for 1-d scalar conservation laws with non uniform convex flux, Rendiconti del Seminario Matematico della Universita di Padova, vol.4, pp.1-24, 2014.

M. Adimurthi, G. D. Singh, and . Veerappa-gowda, Lax-Ole?nik explicit formula and structure theory for balance laws, J. Differential Equations, 2019.

L. Ambrosio, N. Fusco, and D. Pallara, Functions of bounded variation and free discontinuity problems, 2000.

B. Andreianov, C. Donadello, S. S. Ghoshal, and U. Razafison, On the attainability set for triangular type system of conservation laws with initial data control, J. Evol. Equ, vol.15, pp.503-532, 2015.

S. Bianchini and E. Marconi, On the concentration of entropy for scalar conservation laws, Discrete Contin. Dyn. Syst. Ser. S, vol.9, issue.1, pp.73-88, 2016.

S. Bianchini and E. Marconi, On the structure of L ? entropy solutions to scalar conservation laws in one-space dimension, Arch. Mech. Anal, vol.226, issue.1, pp.441-493, 2017.

F. Bouchut and F. James, One-dimensional transport equations with discontinuous coefficients, Nonlinear Analysis TMA, vol.32, pp.891-933, 1998.

F. Bouchut and F. James, Duality solutions for pressureless gases, monotone scalar conservations laws ans uniqueness, Comm. Partial Diff. Eqn, vol.24, pp.2173-2189, 1999.

C. Bourdarias, A. Choudhury, B. Guelmame, and S. Junca, Entropy solutions in BV s for a class of triangular systems involving a transport equation, 2020.
URL : https://hal.archives-ouvertes.fr/hal-02895603

C. Bourdarias, M. Gisclon, and S. Junca, Fractional BV spaces and first applications to conservation laws, J. Hyperbolic Differ. Equ, vol.11, issue.4, pp.655-677, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00785747

C. Bourdarias, M. Gisclon, S. Junca, and Y. Peng, Eulerian and Lagrangian formulations in BV s for gas-solid chromatography, Commun. Math. Sci, vol.14, issue.6, pp.1665-1685, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01258286

A. Bressan, Hyperbolic systems of conservation laws: the one-dimensional Cauchy problem, 2000.

M. Bruneau, La variation totale d'une fonction. (French), Lecture Notes in Mathematics, vol.413, p.p, 1974.

P. Castelli, P. Jabin, and S. Junca, Fractional spaces and conservation laws, Springer Proceedings in Mathematics & Statistics, vol.236, pp.285-293, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01407099

P. Castelli and S. Junca, Oscillating waves and the maximal smoothing effect for one dimensional nonlinear conservation laws, AIMS on Applied Mathematics, vol.8, pp.709-716, 2014.

P. Castelli and S. Junca, Smoothing effect in BV ? ? for entropy solutions of scalar conservation laws, J. Math. Anal. Appl, vol.451, issue.2, pp.712-735, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01133725

P. Castelli and S. Junca, On the maximal smoothing effect for multidmensional scalar conservation laws, Nonlinear Anal, vol.155, pp.207-218, 2017.

K. S. Cheng, The space BV is not enough for hyperbolic conservation laws, J. Math. Anal. Appl, vol.91, issue.2, pp.559-561, 1983.

C. Cheverry, Regularizing effects for multidimensional scalar conservation laws, Ann. Inst. H. Poincar, Anal. Nonlinaire, vol.17, issue.4, pp.413-472, 2000.

G. Crippa, F. Otto, and M. Westdickenberg, Regularizing effect of nonlinearity in multidimensional scalar conservation laws, Transport equations and multi-D hyperbolic conservation laws, Lect. Notes Unione Mat. Ital, vol.5, pp.77-128, 2008.

C. D. Lellis, Blowup of the BV norm in the multidimensional Keyfitz and Kranzer system, Duke Math. J, vol.127, pp.313-339, 2005.

C. De-lellis and M. Westdickenberg, On the optimality of velocity averaging lemmas, Ann. Inst. H. Poincar, Anal. Nonlinaire, vol.20, issue.6, pp.1075-1085, 2003.

B. Gess and X. Lamy, Regularity of solutions to scalar conservation laws with a force, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.36, issue.2, pp.505-521, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01591224

S. S. , Optimal results on TV bounds for scalar conservation laws with discontinuous flux, J. Differential Equations, vol.258, pp.980-1014, 2015.

S. S. Ghoshal and A. Jana, Non existence of the BV regularizing effect for scalar conservation laws in several space dimension, 2019.

E. Giusti, Minimal surfaces and functions of bounded variation, Monographs in Mathematics, vol.80, 1984.

B. Guelmame, S. Junca, and D. Clamond, Regularizing effect for conservation laws with a Lipschitz convex flux, Commun. Math. Sci, vol.17, issue.8, pp.2223-2238, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01943834

P. E. Jabin, Some regularizing methods for transport equations and the regularity of solutions to scalar conservation laws, SéminaireÉquations aux dérivées partielles, 2008.

S. Junca, High frequency waves and the maximal smoothing effect for nonlinear scalar conservation laws, SIAM J. Math. Anal, vol.46, issue.3, pp.2160-2184, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00576662

S. Junca and B. Lombard, Analysis of a Sugimoto's model of nonlinear acoustics in an array of Helmholtz resonators, to appear in SIAM, J. Appl. Math, p.2186692

B. L. Keyfitz and H. C. Kranzer, A system of nonstrictly hyperbolic conservation laws arising in elasticity theory, Arch. Rational Mech. Anal, vol.72, pp.219-241, 1979.

S. N. Kru?kov, First-order quasilinear equations with several space variables, Math. USSR Sbornik, vol.123, pp.217-273, 1970.

P. D. Lax, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math, vol.10, issue.4, pp.537-566, 1957.

P. Lions, B. Perthame, and E. Tadmor, A kinetic formulation of multidimensional scalar conservation laws and related equations, J. Amer. Math. Soc, vol.7, pp.169-192, 1994.

E. Marconi, Regularity estimates for scalar conservation laws in one space dimension, J. Hyperbolic Differ. Eq, vol.15, issue.4, pp.623-691, 2018.

E. Marconi, Structure and regularity of solutions to 1D scalar conservation laws, Proceedings, pp.549-556, 2018.

J. Musielak and W. Orlicz, On generalized variations, I. Studia Math, vol.18, pp.11-41, 1959.

O. Ole?nik, Discontinuous solutions of nonlinear differential equations, Transl. Amer. Math. Soc. Ser, vol.2, issue.26, pp.95-172, 1963.

E. Y. Panov, Existence of strong traces for generalized solutions of multidimensional scalar conservation laws, J. Hyperbolic Differ. Equ, issue.04, pp.885-908, 2005.

E. Y. Panov, Existence of strong traces for quasi-solutions of multidimensional conservation laws, J. Hyperbolic Differ. Equ, vol.4, issue.04, pp.729-770, 2007.

E. Tadmor and T. Tao, Velocity averaging, kinetic formulations and regularizing effects in quasi-linear PDEs, Comm. Pure Appl. Math, vol.60, issue.10, pp.1488-1521, 2007.