H. Amann, M. Hieber, and G. Simonett, Bounded H 1 -calculus for elliptic operators ,D i ?.I n t, E q, vol.7, pp.613-653, 1994.

H. Amann, Compact embeddings of vector-valued Sobolev and Besov spaces, Glass. Mat., III. Ser, vol.35, issue.55, pp.161-177, 2000.

H. Amann, Linear and Quasilinear Parabolic Problems, 1995.
DOI : 10.1007/978-3-0348-9221-6

L. Ambrosio, N. Fusco, and D. Pallara, Free Discontinuity Problems and Special Functions with Bounded Variation, 2000.
DOI : 10.1007/978-3-0348-8974-2_2

M. T. Barlow, One Dimensional Stochastic Differential Equations with No Strong Solution, Journal of the London Mathematical Society, vol.2, issue.2, pp.335-347, 1982.
DOI : 10.1112/jlms/s2-26.2.335

URL : http://jlms.oxfordjournals.org/cgi/content/short/s2-26/2/335

C. Bauzet, G. Vallet, and P. Wittbolt, THE CAUCHY PROBLEM FOR CONSERVATION LAWS WITH A MULTIPLICATIVE STOCHASTIC PERTURBATION, Journal of Hyperbolic Differential Equations, vol.09, issue.04, pp.661-709, 2012.
DOI : 10.1142/S0219891612500221

URL : https://hal.archives-ouvertes.fr/hal-01309552

F. Berthelin and J. Vovelle, Abstract, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.140, issue.05, pp.953-972, 2010.
DOI : 10.1017/S030821050900105X

Z. Brze´zniakbrze´zniak, On stochastic convolution in banach spaces and applications, Stochastics and Stochastic Reports, vol.1180, issue.3-4, pp.245-295, 1997.
DOI : 10.1016/0022-0396(82)90075-4

Z. Brze´zniakbrze´zniak, Stochastic partial differential equations in M-type 2 Banach spaces, Potential Anal, pp.1-45, 1995.

Z. Brze´zniakbrze´zniak and M. Ondreját, Strong solutions to stochastic wave equations with values in Riemannian manifolds, Journal of Functional Analysis, vol.253, issue.2, pp.449-481, 2007.
DOI : 10.1016/j.jfa.2007.03.034

J. Carrillo, Entropy Solutions for Nonlinear Degenerate Problems, Archive for Rational Mechanics and Analysis, vol.147, issue.4, pp.269-361, 1999.
DOI : 10.1007/s002050050152

G. Q. Chen and B. Perthame, 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

G. Da-prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions,E n c y clopedia, Math. Appl, vol.44, 1992.

A. Debussche and J. Vovelle, Scalar conservation laws with stochastic forcing, Journal of Functional Analysis, vol.259, issue.4, pp.1014-1042, 2010.
DOI : 10.1016/j.jfa.2010.02.016

URL : https://hal.archives-ouvertes.fr/hal-00451641

R. J. Diperna and P. L. , Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math, pp.98-511, 1989.

R. M. Dudley, Real Analysis and Probability, 2002.
DOI : 10.1017/CBO9780511755347

R. E. Edwards, Functional Analysis, Theory and Applications, 1965.

J. Feng and D. Nualart, Stochastic scalar conservation laws, Journal of Functional Analysis, vol.255, issue.2, pp.313-373, 2008.
DOI : 10.1016/j.jfa.2008.02.004

F. Flandoli, Dirichlet boundary value problem for stochastic parabolic equations: compatibility relations and regularity of solutions, Stochastics An International Journal of Probability and Stochastic Processes, vol.29, issue.3, pp.331-357, 1990.
DOI : 10.1080/17442509008833620

F. Flandoli and D. Ga¸tarekga¸tarek, Martingale and stationary solutions for stochastic Navier-Stokes equations, Probability Theory and Related Fields, vol.46, issue.5, pp.367-391, 1995.
DOI : 10.1007/BF01192467

F. Flandoli, M. Gubinelli, and E. Priola, Well-posedness of the transport equation by??stochastic perturbation, Inventiones mathematicae, vol.93, issue.135, pp.1-53, 2010.
DOI : 10.1007/s00222-009-0224-4

URL : https://hal.archives-ouvertes.fr/hal-00359723

M. I. Freidlin, On the factorization of nonnegative definite matrices, Theory Probability Appl, pp.354-356, 1968.

A. Friedman, Partial Differential Equations of Parabolic Type, 1964.

G. Gagneux and M. Madaune-tort, Analyse mathématique de modèles non linéaires de l'ingénieriepétrolì ere, 1996.

D. Ga¸tarekga¸tarek and B. , On weak solutions of stochastic equations in Hilbert spaces, Stochastics An International Journal of Probability and Stochastic Processes, vol.46, issue.1, pp.41-51, 1994.
DOI : 10.1080/17442509408833868

H. C. Grunau and W. Wahl, Regularity of weak solutions of semilinear parabolic systems of arbitrary order, Journal d'Analyse Math??matique, vol.25, issue.1, pp.307-322, 1994.
DOI : 10.1007/BF02835960

I. Gyöngy and N. Krylov, Existence of strong solutions for It???'s stochastic equations via approximations, Probability Theory and Related Fields, vol.1, issue.2, pp.143-158, 1996.
DOI : 10.1007/BF01203833

I. Gyöngy and C. Rovira, On L p -solutions of semilinear stochastic partial differential equations, Stochastic Process, Appl, vol.90, pp.83-108, 2000.

M. Hofmanová, A Bhatnagar???Gross???Krook approximation to stochastic scalar conservation laws, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.51, issue.4
DOI : 10.1214/14-AIHP610

M. Hofmanová, Degenerate parabolic stochastic partial differential equations, Stochastic Processes and their Applications, vol.123, issue.12
DOI : 10.1016/j.spa.2013.06.015

M. Hofmanová, Strong solutions of semilinear stochastic partial differential equations, Nonlinear Di?er, Equ. Appl, vol.20, issue.3, pp.757-778, 2013.

M. Hofmanová and J. Seidler, On Weak Solutions of Stochastic Differential Equations, Stochastic Analysis and Applications, vol.2, issue.1, pp.100-121, 2012.
DOI : 10.1080/07362994.2012.628916

M. Hofmanová and J. Seidler, On Weak Solutions of Stochastic Differential Equations II, Stochastic Analysis and Applications, vol.31, issue.4
DOI : 10.1007/978-3-642-23280-0

H. Holden and N. H. Risebro, Conservation laws with a random source, Applied Mathematics & Optimization, vol.148, issue.2, pp.229-241, 1997.
DOI : 10.1007/BF02683344

N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, 1989.

C. Imbert and J. Vovelle, A Kinetic Formulation for Multidimensional Scalar Conservation Laws with Boundary Conditions and Applications, SIAM Journal on Mathematical Analysis, vol.36, issue.1, pp.214-232, 2004.
DOI : 10.1137/S003614100342468X

URL : https://hal.archives-ouvertes.fr/hal-00176541

K. Itô, On a stochastic integral equation, Proceedings of the Japan Academy, vol.22, pp.1-4, 1946.

K. Itô, On stochastic differential equations, Memoirs of the American Mathematical Society, vol.4, pp.1-51, 1951.

I. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus, 1988.

R. Khasminskii, Stochastic Stability of Differential Equations

J. U. Kim, On a stochastic scalar conservation law, Indiana Univ, Math. J, vol.52, issue.1, pp.227-256, 2003.

S. N. Kru?kov, 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

N. V. Krylov and B. L. Rozovskii, ON THE CAUCHY PROBLEM FOR LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS, Mathematics of the USSR-Izvestiya, vol.11, issue.6, pp.1329-1347, 1977.
DOI : 10.1070/IM1977v011n06ABEH001768

N. V. Krylov and B. L. Rozovskii, Stochastic evolution equations, Itogi Nauki i Tekhniki, Ser. Sovrem. Probl. Mat. English transl. J. Sov. Math, vol.14, issue.164, pp.71-146, 1979.

H. Kunita, Stochastic differential equations and stochastic flows of diffeomorphisms, Lecture Notes in Math, vol.47, pp.143-303, 1984.
DOI : 10.1007/BF00535284

H. Kunita, Stochastic flows and stochastic differential equations, 1990.

O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. , Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs 23, Am. Math. Soc, 1968.

G. M. Lieberman, Second Order Parabolic Differential Equations, 1996.
DOI : 10.1142/3302

P. L. Lions, B. Perthame, and E. Tadmor, Formulation cinétique des lois de conservation scalaires multidimensionnelles, C.R. Acad. Sci. Paris, pp.97-102, 1991.

P. L. Lions, B. Perthame, and E. Tadmor, 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

J. Málek, J. Ne?as, M. Rokyta, and M. R??i?ka, Weak and Measure-valued Solutions to Evolutionary PDEs, 1996.
DOI : 10.1007/978-1-4899-6824-1

A. Nouri, A. Omrane, and J. P. Vila, Erratum on ???Boundary Conditions for Scalar Conservation Laws, from a Kinetic Point of View???, Journal of Statistical Physics, vol.115, issue.5/6, pp.5-6, 1999.
DOI : 10.1023/B:JOSS.0000028246.81983.ba

A. Nouri, A. Omrane, and J. P. Vila, Erratum on ???Boundary Conditions for Scalar Conservation Laws, from a Kinetic Point of View???, Journal of Statistical Physics, vol.115, issue.5/6, pp.5-6, 2004.
DOI : 10.1023/B:JOSS.0000028246.81983.ba

M. Ondreját, Stochastic nonlinear wave equations in local Sobolev spaces,E l e c tronic, Journal of Probability, vol.15, issue.33, pp.1041-1091, 2010.

M. Ondreját, Uniqueness for stochastic evolution equations in Banach spaces, Dissertationes Mathematicae, vol.426, pp.1-63, 2004.
DOI : 10.4064/dm426-0-1

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equation, Applied Mathematical Sciences, vol.44, 1983.
DOI : 10.1007/978-1-4612-5561-1

B. Perthame, Uniqueness and error estimates in first order quasilinear conservation laws via the kinetic entropy defect measure, Journal de Math??matiques Pures et Appliqu??es, vol.77, issue.10, pp.1055-1064, 1998.
DOI : 10.1016/S0021-7824(99)80003-8

B. Perthame, Kinetic Formulation of Conservation Laws, Oxford Lecture Ser, Math. Appl, vol.21, 2002.

B. Perthame and E. Tadmor, A kinetic equation with kinetic entropy functions for scalar conservation laws, Communications in Mathematical Physics, vol.81, issue.3, pp.501-517, 1991.
DOI : 10.1007/BF02099071

R. S. Philips and L. Sarason, Elliptic-parabolic equations of the second order, J . Math. Mach, vol.17, pp.891-917, 1968.

P. E. Protter, Stochastic Integration and Differential Equations, 2004.

T. Runst and W. Sickel, Sobolev Spaces of Fractional Order, Nemytskij Operators , and Nonlinear Partial Differential Equations, de Gruyter Series in Nonlinear Analysis and Applications, I. Marichev, Fractional Integrals and Derivatives , Gordon and Breach, 1993.

B. Saussereau and I. L. Stoica, Scalar conservation laws with fractional stochastic forcing: Existence, uniqueness and invariant measure, Stochastic Processes and their Applications, vol.122, issue.4, pp.1456-1486, 2012.
DOI : 10.1016/j.spa.2012.01.005

A. V. Skorokhod, On existence and uniqueness of solutions to stochastic diffusion equations, Russian) Sibirski? ? Matematicheski? ? Zhurnal, pp.129-137, 1961.

A. V. Skorokhod, On stochastic differential equations, Russian) In Proceedings of the 6th All-Union Conference on Probability Theory and Mathematical Statistics, GIPNL Litovsko? ? SSR, Vil'nyus, pp.159-168, 1962.

G. Vallet and P. Wittbolt, ON A STOCHASTIC FIRST-ORDER HYPERBOLIC EQUATION IN A BOUNDED DOMAIN, Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol.12, issue.04, pp.613-651, 2009.
DOI : 10.1142/S0219025709003872

URL : https://hal.archives-ouvertes.fr/hal-00866266

W. Wahl, Extension of a result of Ladyzhenskaya and Ural'ceva concerning second order parabolic equations of arbitrary order, Ann. Pol. Math, pp.41-63, 1983.

E. Weinan, K. Khanin, A. Mazel, and Y. Sinai, Invariant measures for Burgers equation with stochastic forcing, Annals of Mathematics, vol.151, pp.877-960, 2000.
DOI : 10.1007/978-1-4419-6205-8_17

A. Yagi, Abstract Parabolic Evolution Equations and their Applications, 2010.
DOI : 10.1007/978-3-642-04631-5

X. Zhang, Smooth solutions of non-linear stochastic partial differential equations driven by multiplicative noises, Science China Mathematics, vol.249, issue.11, pp.2949-2972, 2010.
DOI : 10.1007/s11425-010-4058-8

X. Zhang, Regularities for semilinear stochastic partial differential equations, Journal of Functional Analysis, vol.249, issue.2, pp.454-476, 2007.
DOI : 10.1016/j.jfa.2007.03.018