, To check that the triangular system (1.1),(1.2) is not a Temple system, vol.67

, To obtain the cubic estimate on the global Rankine-Hugoniot curve below

, To obtain the existence result, bounding Z along the 2-characteristics

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

A. Fabio, O. Glass, and K. T. Nguyen, On Kolmogorov entropy compactness estimates for scalar conservation laws without uniform convexity, SIAM J. Math. Anal, vol.51, issue.4, pp.3020-3051, 2019.

F. Ancona and A. Marson, Well-posedness for general 2 × 2 systems of conservation laws, Mem. Amer. Math. Soc, vol.169, issue.801, p.170, 2004.

F. Ancona and A. Marson, A locally quadratic Glimm functional and sharp convergence rate of the Glimm scheme for nonlinear hyperbolic systems, Arch. Ration. Mech. Anal, vol.196, issue.2, pp.455-487, 2010.

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.

P. Baiti and H. K. Jenssen, Well-posedness for a class of 2 × 2 conservation laws with L ? data, J. Differential Equations, vol.140, issue.1, pp.161-185, 1997.

S. Bianchini, On the Riemann problem for nonconservative hyperbolic systems, Preprint I.A.C, 2002.

S. Bianchini, R. Colombo, and F. Monti, 2 × 2 systems of conservation laws with L ? data, J. Differential Equations, vol.249, issue.12, pp.3466-3488, 2010.

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, Ar. Mech. Anal, vol.226, issue.1, pp.441-493, 2017.

F. Bouchut and F. James, Equations de transport unidimensionnellesà coefficients discontinus, C. R. Acad. Sci. Paris Série I, vol.320, pp.1097-1102, 1995.

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. Eq, vol.24, pp.2173-2189, 1999.

C. Bourdarias, M. Gisclon, and S. Junca, Some mathematical results on a system of transport equations with an algebraic constraint describing fixed-bed adsorption of gases, J. Math. Anal. Appl, vol.313, issue.2, pp.551-571, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00387187

C. Bourdarias, M. Gisclon, and S. Junca, Existence of entropy solutions for gas chromatography with one or two actives species and non convex isotherms, Commun. Math. Sci, vol.5, issue.1, pp.67-84, 2007.

C. Bourdarias, M. Gisclon, and S. Junca, Hyperbolic models in gas-solid chromatography, Bol. Soc. Esp. Mat. Apl, vol.43, pp.29-57, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00387202

C. Bourdarias, M. Gisclon, and S. Junca, Strong stability with respect to weak limit for a hyperbolic system arising from gas chromatography, Methods and Applications of Analysis, vol.17, issue.3, pp.301-330, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00387499

C. Bourdarias, M. Gisclon, and S. Junca, Blow up at the hyperbolic boundary for a 2 × 2 chemical system, J. Hyperbolic Differ. Equ, vol.7, issue.2, pp.297-316, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00403226

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, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01258286

Y. Brenier and E. Grenier, Sticky particles and scalar conservation laws, SIAM J. Numer. Anal, vol.35, issue.6, pp.2317-2328, 1998.

A. Bressan, Hyperbolic Systems of Conservation Laws, The One-Dimensional Cauchy Problem, vol.20, 2000.

M. Bruneau, Étude et généralisation d'une classe de fonctions lipschitziennes très irrégulières. (French), 1970.

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

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

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

R. Colombo and A. Corli, On 2 × 2 conservation laws with large data, NoDEA, vol.10, pp.255-268, 2003.

C. Dafermos, Polygonal approximations of solutions of the initial value problem for a conservation law, J. M. A. A, vol.38, pp.33-41, 1972.

C. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, 2000.

C. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, 2016.

C. De-lellis, F. Otto, and M. Westdickenberg, Structure of entropy solutions for multidimensional scalar conservation laws, Arch. Ration. Mech. Anal, vol.170, issue.2, pp.137-184, 2003.

C. De-lellis and T. Rivière, The rectifiability of entropy measures in one space dimension, J. Math. Pures Appl, vol.82, issue.9, pp.1343-1367, 2003.

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

R. Diperna, Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Anal, vol.82, issue.1, pp.27-70, 1983.

M. Douglas-levan, C. Costa, A. Rodrigues, A. Bossy, and D. Tondeur, Fixedbed adsorption of gases: Effect of velocity variations on transition types, AIChE Journal, vol.34, issue.6, pp.996-1005, 1988.

S. Ghoshal, B. Guelmame, A. Jana and S. Junca, Optimal regularity for all time for entropy solutions of conservation laws in $BV^s$, 2020.
URL : https://hal.archives-ouvertes.fr/hal-02495036

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

J. Glimm and P. D. , Lax Decay of solutions of systems of hyperbolic conservation laws, Mem. A.M.S, vol.101, 1970.

B. T. Hayes and P. G. Lefloch, Measure solutions to a strictly hyperbolic system of conservation laws, Nonlinearity, vol.9, issue.6, pp.1547-1563, 1996.

B. Haspot and S. Junca, BV s solutions for 2 × 2 systems of conservation laws with a linearly degenerate field, vol.2020, p.2532444

H. Holden, On the strict hyperbolicity of the Buckley-Leverett equations for threephase flow. Nonlinear evolution equations that change type, Math. Appl, vol.27, pp.79-84, 1990.

H. Holden and N. H. Risebro, Front tracking for hyperbolic conservation laws, Applied Mathematical Sciences, vol.152, 2015.

T. Igushi and P. L. Floch, Existence theory for hyperbolic systems of conservation laws with general flux fonctions, Arch. Rational Mech. Anal, vol.168, pp.165-244, 2003.

P. Jabin, Some regularizing methods for transport equations and the regularity of solutions to scalar conservation laws, Séminaire: Equations aux Dérivées Partielles, 2010.

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 Helmholt resonators, Appl. Math, p.2186692

B. Keyfitz, B. , and H. C. Kranzer, A strictly hyperbolic system of conservation laws admitting singular shocks. Nonlinear evolution equations that change type, Math. Appl, vol.27, pp.107-125, 1990.

S. N. Kruzkov, First order quasilinear equations with several independent variables. (Russian) Mat. Sb, N.S.), vol.81, issue.123, pp.228-255, 1970.

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

P. G. Lefloch, An existence and uniqueness result for two nonstrictly hyperbolic systems. Nonlinear evolution equations that change type, Math. Appl, vol.27, pp.126-138, 1990.

P. G. Lefloch, Hyperbolic Systems of Conservation Laws: the theory of classical and nonclassical shock waves, Lectures in Mathematics, 2002.

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.

W. Neves and D. Serre, Ill-posedness of the Cauchy problem for totally degenerate system of conservation laws. Electron, J. Differ. Equ, vol.25, issue.124, p.p, 2005.

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

Y. Peng, Explicit solutions for 2 × 2 linearly degenerate systems, Appl. Math. Lett, vol.11, issue.5, pp.75-78, 1998.

Y. Peng, Euler-Lagrange change of variables in conservation laws, Nonlinearity, vol.20, issue.8, pp.1927-1953, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00488988

F. Poupaud and M. Rascle, Measure solutions to the linear multi-dimensional transport equation with non-smooth coefficients, Comm. Partial Differential Equations, vol.22, issue.1-2, pp.337-358, 1997.

H. Rhee, R. Aris, and N. R. Amundson, On the theory of multicomponent chromatography, Philos. Trans. Roy. Soc. A, issue.267, pp.419-455, 1970.

P. Rouchon, M. Sghoener, P. Valentin, and G. Guiochon, Numerical Simulation of Band Propagation in Nonlinear Chromatography, Chromatographic Science Series, vol.46, 1988.

D. Serre, Systems of conservation laws. I: Hyperbolicity, entropy, shock waves. (Systèmes de lois de conservation. I: Hyperbolicité, entropies, ondes de choc.) (French) Fondations. Paris: Diderot Editeur. xii, vol.298, p.p, 1996.
URL : https://hal.archives-ouvertes.fr/ensl-01402415

J. Smoller, Shock waves and reaction-diffusion equations

G. Der-mathematischen-wissenschaften, , p.258, 1994.

M. Sever, Large-data solution of a model system for singular shocks, J. Hyperbolic Differ. Equ, vol.7, issue.4, pp.775-840, 2010.

B. Temple, Systems of conservation laws with invariant submanifolds, Trans. Amer. Soc, vol.280, pp.781-795, 1993.

D. Wagner, Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions, J. Differential Equations, vol.68, issue.1, pp.118-136, 1987.