]. B. Bibliographie1 and . Andreianov, Time compactness tools for discretized evolution equations and applications to degenerate parabolic PDEs In Finite volumes for complex applications VI. Problems & perspectives, of Springer Proc. Math, pp.21-29, 2011.

B. Andreianov, M. Bendahmane, and K. H. Karlsen, DISCRETE DUALITY FINITE VOLUME SCHEMES FOR DOUBLY NONLINEAR DEGENERATE HYPERBOLIC-PARABOLIC EQUATIONS, Journal of Hyperbolic Differential Equations, vol.3, issue.01, pp.1-67, 2010.

B. Andreianov, F. Boyer, and F. Hubert, Discrete duality finite volume schemes for Leray???Lions???type elliptic problems on general 2D meshes, Numerical Methods for Partial Differential Equations, vol.152, issue.1, pp.145-195, 2007.

B. Andreianov, C. Cancès, and A. Moussa, A nonlinear time compactness result and applications to discretization of degenerate parabolic???elliptic PDEs, Journal of Functional Analysis, vol.273, issue.12, p.1142499, 2015.

B. Andreianov, R. Eymard, M. Ghilani, and N. Marhraoui, Finite volume approximation of degenerate two-phase flow model with unlimited air mobility, Numerical Methods for Partial Differential Equations, vol.3, issue.2, pp.441-474, 2013.

B. Andreianov, M. Gutnic, and P. Wittbold, Convergence of Finite Volume Approximations for a Nonlinear Elliptic-Parabolic Problem: A "Continuous" Approach, SIAM Journal on Numerical Analysis, vol.42, issue.1, pp.228-251, 2004.

B. Andreianov and P. Wittbold, Convergence of approximate solutions to an elliptic???parabolic equation without the structure condition, Nonlinear Differential Equations and Applications NoDEA, vol.131, issue.1, pp.695-717, 2012.

O. Angelini, K. Brenner, and D. Hilhorst, A finite volume method on general meshes for a degenerate parabolic convection???reaction???diffusion equation, Numerische Mathematik, vol.197, issue.9???12, pp.219-257, 2013.

A. Attaoui, D. Blanchard, and O. Guibé, Weak-renormalized solution for a nonlinear Boussinesq system, Differential Integral Equations, vol.22, pp.5-6465, 2009.

A. , B. Cheikh, and O. Guibé, Résultats d'existence et d'unicité pour une classe de problèmes non linéaires et non coercifs, C. R. Acad. Sci. Paris Sér. I Math, vol.329, issue.11, pp.967-972, 1999.

A. , B. Cheikh, and O. Guibé, Nonlinear and non-coercive elliptic problems with integrable data, Adv. Math. Sci. Appl, vol.16, issue.1, pp.275-297, 2006.

P. Bénilan, L. Boccardo, T. Gallouët, R. Gariepy, M. Pierre et al., An L 1 -theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci, issue.42, pp.22241-273, 1995.

M. Bessemoulin-chatard, C. Chainais-hillairet, and F. Filbet, On discrete functional inequalities for some finite volume schemes, IMA Journal of Numerical Analysis, vol.35, issue.3, pp.1125-1149, 2015.

D. Blanchard, Renormalized solutions for parabolic problems with L 1 data In Free boundary problems, theory and applications, Pitman Res. Notes Math. Ser, vol.363, pp.177-185, 1995.

D. Blanchard and O. Guibé, Existence of a solution for a nonlinear system in thermoviscoelasticity, Adv. Differential Equations, vol.5, pp.10-121221, 2000.

D. Blanchard, O. Guibé, and H. Redwane, Existence and uniqueness of a solution for a class of parabolic equations with two unbounded nonlinearities, Commun. Pure Appl. Anal, vol.15, issue.1, pp.197-217, 2016.

D. Blanchard and F. Murat, Renormalised solutions of nonlinear parabolic problems with L1 data: existence and uniqueness, Proc. Roy. Soc. Edinburgh Sect. A, pp.1137-1152, 1997.

D. Blanchard, F. Murat, and H. Redwane, Existence and Uniqueness of a Renormalized Solution for a Fairly General Class of Nonlinear Parabolic Problems, Journal of Differential Equations, vol.177, issue.2, pp.331-374, 2001.

D. Blanchard and A. Porretta, Nonlinear parabolic equations with natural growth terms and measure initial data, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.30, issue.4, pp.3-4583, 2001.

D. Blanchard and A. Porretta, Stefan problems with nonlinear diffusion and convection, Journal of Differential Equations, vol.210, issue.2, pp.383-428, 2005.

D. Blanchard and H. Redwane, Renormalized solutions for a class of nonlinear evolution problems, Journal de Math??matiques Pures et Appliqu??es, vol.77, issue.2, pp.117-151, 1998.

L. Boccardo, A. Dall-'aglio, T. Gallouët, and L. Orsina, Nonlinear Parabolic Equations with Measure Data, Journal of Functional Analysis, vol.147, issue.1, pp.237-258, 1997.

L. Boccardo and T. Gallouët, Non-linear elliptic and parabolic equations involving measure data, Journal of Functional Analysis, vol.87, issue.1, pp.149-169, 1989.

L. Boccardo and T. Gallouët, Nonlinear Elliptic Equations with Right Hand Side Measures, Communications in Partial Differential Equations, vol.15, issue.3-4, pp.641-655, 1992.
DOI : 10.5802/aif.204

L. Boccardo, T. Gallouët, and F. Murat, Unicité de la solution de certaines équations elliptiques non linéaires, C. R. Acad. Sci. Paris Sér. I Math, issue.11, pp.3151159-1164, 1992.

J. Carrillo and M. Chipot, Synopsis, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.287, issue.3-4, pp.3-4281, 1985.

J. Casado-dí-az, T. Chacón-rebollo, V. Girault, M. G. Mármol, and F. Murat, Finite elements approximation of second order linear elliptic equations in divergence form with right-hand side in L 1, Numerische Mathematik, vol.15, issue.3, pp.337-374, 2007.
DOI : 10.5802/aif.204

C. Chainais-hillairet, J. Droniou-]-k, S. Che?mi?ski, and . Owczarek, Finite-volume schemes for noncoercive elliptic problems with Neumann boundary conditions, IMA Journal of Numerical Analysis, vol.31, issue.1, pp.61-85643, 2011.

K. Che?mi?ski and S. Owczarek, Renormalized solutions in thermo-visco-plasticity for a Norton???Hoff type model. Part I: The truncated case, Nonlinear Analysis: Real World Applications, vol.28, pp.140-152, 2016.

K. Che?mi?ski and S. Owczarek, Renormalized solutions in thermo-visco-plasticity for a Norton???Hoff type model. Part I: The truncated case, Nonlinear Analysis: Real World Applications, vol.28, issue.37, pp.140-152489, 2016.

Y. Coudière, T. Gallouët, and R. Herbin, error estimates for finite volume solutions of convection diffusion equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.13, issue.4, pp.767-778, 2001.
DOI : 10.1137/0913073

G. Dal-maso, F. Murat, L. Orsina, and A. Prignet, Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.28, issue.44, pp.741-808, 1999.

R. , D. Nardo, F. Feo, and O. Guibé, Existence result for nonlinear parabolic equations with lower order terms, Anal. Appl. (Singap.), vol.9, issue.2, pp.161-186, 2011.

R. , D. Nardo, F. Feo, and O. Guibé, Uniqueness of renormalized solutions to nonlinear parabolic problems with lower-order terms, Proc. Roy. Soc. Edinburgh Sect. A, vol.143, issue.6, pp.1185-1208, 2013.

R. J. Diperna and P. L. Lions, On the Cauchy Problem for Boltzmann Equations: Global Existence and Weak Stability, The Annals of Mathematics, vol.130, issue.2, pp.321-366, 1989.
DOI : 10.2307/1971423

J. Droniou, Solving convection-diffusion equations with mixed, Neumann and Fourier boundary conditions and measures as data, by a duality method, Adv. Differential Equations, vol.5, pp.10-121341, 2000.

J. Droniou, Global and Local Estimates for Nonlinear Noncoercive Elliptic Equations with Measure Data, Communications in Partial Differential Equations, vol.329, issue.11, pp.129-153, 2003.

J. Droniou, Finite volume schemes for fully non-linear elliptic equations in divergence form, ESAIM: Mathematical Modelling and Numerical Analysis, vol.58, issue.6, pp.1069-1100, 2006.

J. Droniou, T. Gallouët, and R. Herbin, A Finite Volume Scheme for a Noncoercive Elliptic Equation with Measure Data, SIAM Journal on Numerical Analysis, vol.41, issue.6, pp.1997-2031, 2003.

J. Droniou and J. L. Vázquez, Noncoercive convection???diffusion elliptic problems with Neumann boundary conditions, Calculus of Variations and Partial Differential Equations, vol.11, issue.4, pp.413-434, 2009.

E. Emmrich and D. Siska, Full discretisation of second-order nonlinear evolution equations: strong convergence and applications, Computational Methods in Applied Mathematics, vol.11, issue.4, pp.441-459, 2011.

E. Emmrich and M. Thalhammer, Doubly nonlinear evolution equations of second order: Existence and fully discrete approximation, Journal of Differential Equations, vol.251, issue.1, pp.82-118, 2011.

R. Eymard, T. Gallouët, and R. Herbin, Finite volume methods, VII, Handb. Numer. Anal., VII, pp.713-1020, 2000.

R. Eymard, T. Gallouët, R. Herbin, and A. Michel, Convergence of a finite volume scheme for nonlinear degenerate parabolic equations, Numerische Mathematik, vol.92, issue.1, pp.41-82, 2002.

T. Gallouët and R. Herbin, Finite volume approximation of elliptic problems with irregular data, Finite volumes for complex applications II, pp.155-162, 1999.

T. Gallouët, A. Larcher, and J. C. Latché, Convergence of a finite volume scheme for the convection-diffusion equation with $\mathrm{L}^{1}$ data, Mathematics of Computation, vol.81, issue.279, pp.1429-1454, 2012.

T. Gallouët and J. C. Latché, Compactness of discrete approximate solutions to parabolic PDEs - Application to a turbulence model, Communications on Pure and Applied Analysis, vol.11, issue.6, pp.2371-2391, 2012.

O. Guibé and A. Mercaldo, Uniqueness results for noncoercive nonlinear elliptic equations with two lower order terms, Commun. Pure Appl. Anal, vol.7, issue.1, pp.163-192, 2008.

R. Landes, On the existence of weak solutions for quasilinear parabolic initialboundary value problems, Proc. Roy. Soc. Edinburgh Sect. A, vol.89, pp.3-4217, 1981.

A. Larcher and J. C. Latché, Convergence analysis of a finite element-finite volume scheme for a rans turbulence model, p.2012

S. Leclavier, Finite volume scheme and renormalized solutions for a noncoercive and nonlinear parabolic problem with L 1 data

S. Leclavier, Abstract, Computational Methods in Applied Mathematics, vol.8, issue.1, pp.85-104, 2017.
DOI : 2819994741808

J. Leray and J. L. Lions, Quelques résultats de Vi?ik sur les problèmes elliptiques nonlinéaires par les méthodes de Minty-Browder, pp.97-107, 1965.

R. Lewandowski, Analyse mathématique et océanographie, Recherches en Mathématiques Appliquées, vol.39, 1997.

J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, 1969.
DOI : 10.1007/bf00249679

P. L. Lions, Mathematical topics in fluid mechanics Incompressible models, of Oxford Lecture Series in Mathematics and its Applications, 1996.

P. L. Lions and F. Murat, Solutions renormarlisées d'équations elliptiques non linéaires

F. Murat, Equations elliptiques non linéaires avec second membre L 1 ou mesure, Compte Rendu du 26ème Congrès d'Analyse Numérique, 1994.

F. Otto, L1-Contraction and Uniqueness for Quasilinear Elliptic???Parabolic Equations, Journal of Differential Equations, vol.131, issue.1, pp.20-38, 1996.

I. Paw?ow and W. M. Zajczkowski, Global Regular Solutions to a Kelvin--Voigt Type Thermoviscoelastic System, SIAM Journal on Mathematical Analysis, vol.45, issue.4, pp.1997-2045, 2013.
DOI : 10.1137/110859026

F. Petitta, A. Ponce, and A. Porretta, Diffuse measures and nonlinear parabolic equations, Journal of Evolution Equations, vol.177, issue.4, pp.861-905, 2011.
DOI : 10.1007/BF02505907

F. Petitta and A. Porretta, On the Notion of Renormalized Solution to Nonlinear Parabolic Equations with General Measure Data, Journal of Elliptic and Parabolic Equations, vol.177, issue.4, pp.201-214, 2015.
DOI : 10.1007/BF02505907

A. Prignet, Remarks on existence and uniqueness of solutions of elliptic problems with right-hand side measures, Rend. Mat. Appl, vol.15, issue.73, pp.321-337, 1995.

A. Prignet, Existence and uniqueness of ???entropy??? solutions of parabolic problems with L1 data, Nonlinear Analysis: Theory, Methods & Applications, vol.28, issue.12, pp.1943-1954, 1997.

T. Roubí?ek, Thermo-visco-elasticity at small strains with $L^1$-data, Quarterly of Applied Mathematics, vol.67, issue.1, pp.47-71, 2009.

J. Serrin, Pathological solutions of elliptic differential equations, Ann. Scuola Norm. Sup. Pisa, vol.18, issue.3, pp.385-387, 1964.

J. Simon, Compact sets in the spaceL p (O,T; B), Annali di Matematica Pura ed Applicata, vol.287, issue.1, pp.65-96, 1987.
DOI : 10.5802/aif.68

G. Stampacchia, Le probl??me de Dirichlet pour les ??quations elliptiques du second ordre ?? coefficients discontinus, Annales de l???institut Fourier, vol.15, issue.1, pp.189-258, 1965.
DOI : 10.5802/aif.204

C. Vaz and E. Fernández-cara, Renormalized solutions to a system of type Navier???Stokes, Journal of Mathematical Analysis and Applications, vol.378, issue.2, pp.442-449, 2011.