E. [. Arnold, Q. Carlen, and . Ju, Large-time behavior of non-symmetric Fokker- Planck type equations, Commun. Stoch. Anal, vol.2, issue.1, pp.153-175, 2008.

J. [. Arnold, C. Carrillo, and . Manzini, Refined long-time asymptotics for some polymeric fluid flow models, Communications in Mathematical Sciences, vol.8, issue.3, pp.763-782, 2010.
DOI : 10.4310/CMS.2010.v8.n3.a8

[. Ambrosio, N. Gigli, and G. Savaré, Gradient flows in metric spaces and in the space of probability measures, Lectures in Math. ETH Zürich. Birkhäuser, 2008.

[. Ambrosio, N. Gigli, and G. Savaré, Metric measure spaces with Riemannian Ricci curvature bounded from below, Duke Mathematical Journal, vol.163, issue.7, 2011.
DOI : 10.1215/00127094-2681605
URL : https://hal.archives-ouvertes.fr/hal-00769376

A. Arnold, P. Markowich, G. Toscani, and A. Unterreiter, ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS, Communications in Partial Differential Equations, vol.324, issue.1-2, pp.43-100, 2001.
DOI : 10.1007/s002200050631

D. Bakry, F. Barthe, P. Cattiaux, and A. Guillin, A simple proof of the Poincar?? inequality for a large class of probability measures, Electronic Communications in Probability, vol.13, issue.0, pp.60-66, 2008.
DOI : 10.1214/ECP.v13-1352

V. I. Bogachev, G. Da-prato, and M. Röckner, On Parabolic Equations for Measures, Communications in Partial Differential Equations, vol.28, issue.3, pp.397-418, 2008.
DOI : 10.1007/s00028-004-0147-x

I. [. Bolley, A. Gentil, and . Guillin, Uniform Convergence to Equilibrium for Granular Media, Archive for Rational Mechanics and Analysis, vol.128, issue.2, 2012.
DOI : 10.1007/s00205-012-0599-z
URL : https://hal.archives-ouvertes.fr/hal-00688780

A. [. Bolley, F. Guillin, and . Malrieu, Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation, ESAIM: Mathematical Modelling and Numerical Analysis, vol.44, issue.5, pp.867-884, 2010.
DOI : 10.1051/m2an/2010045
URL : https://hal.archives-ouvertes.fr/hal-00392397

F. Bolley, A. Guillin, and C. Villani, Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces, Probability Theory and Related Fields, vol.206, issue.1, pp.3-4541, 2007.
DOI : 10.1007/s00440-006-0004-7
URL : https://hal.archives-ouvertes.fr/hal-00453883

]. L. Caf92 and . Caffarelli, The regularity of mappings with a convex potential, J. Amer. Math. Soc, vol.5, issue.1, pp.99-104, 1992.

J. A. Carrillo, M. D. Francesco, and G. Toscani, Strict contractivity of the 2- Wasserstein distance for the porous medium equation by mass-centering, Proc. AMS, pp.353-363, 2007.

. [. Cordero-erausquin, Some Applications of Mass Transport to Gaussian-Type Inequalities, Archive for Rational Mechanics and Analysis, vol.161, issue.3, pp.257-269, 2002.
DOI : 10.1007/s002050100185
URL : https://hal.archives-ouvertes.fr/hal-00693655

A. [. Cattiaux and . Guillin, On quadratic transportation cost inequalities, Journal de Math??matiques Pures et Appliqu??es, vol.86, issue.4, pp.341-361, 2006.
DOI : 10.1016/j.matpur.2006.06.003

R. [. Carrillo, C. Mccann, and . Villani, Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media, Archive for Rational Mechanics and Analysis, vol.179, issue.2, pp.217-263, 2006.
DOI : 10.1007/s00205-005-0386-1

G. [. Carrillo and . Toscani, Contractive probability metrics and asymptotic behavior of dissipative kinetic equations, Riv. Mat. Univ. Parma, vol.7, issue.6, pp.75-198, 2007.

]. A. Ebe11 and . Eberle, Reflection coupling and Wasserstein contractivity without convexity, 2011.

C. [. Gozlan and . Léonard, Transport inequalities. A survey, Markov Process. Related Fields, pp.635-736, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00515419

A. Guillin, C. Léonard, F. Y. Wang, and L. Wu, Transportation-information inequalities for Markov processes (II) : relations with other functional inequalities, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00360854

A. Guillin, C. Léonard, L. Wu, and N. Yao, Transportation-information inequalities for Markov processes. Probab. Theory Related Fields, pp.3-4669, 2009.
DOI : 10.1007/s00440-008-0159-5
URL : https://hal.archives-ouvertes.fr/hal-00158258

C. [. Jourdain, T. Le-bris, F. Lelì, and . Otto, Long-Time Asymptotics of a Multiscale Model for Polymeric Fluid Flows, Archive for Rational Mechanics and Analysis, vol.18, issue.1, pp.97-148, 2006.
DOI : 10.1007/s00205-005-0411-4

]. S. Lis09 and . Lisini, Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces, ESAIM Contr. Opt. Calc. Var, vol.15, pp.712-740, 2009.

M. [. Natile, G. Peletier, and . Savaré, Contraction of general transportation costs along solutions to Fokker???Planck equations with monotone drifts, Journal de Math??matiques Pures et Appliqu??es, vol.95, issue.1, pp.18-35, 2011.
DOI : 10.1016/j.matpur.2010.07.003

C. [. Otto and . Villani, Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality, Journal of Functional Analysis, vol.173, issue.2, pp.361-400, 2000.
DOI : 10.1006/jfan.1999.3557

C. [. Otto and . Villani, Comment on Hypercontractivity of Hamilton-Jacobi equations, J. Math. Pures Appl.. J. Math. Pures Appl, vol.80, issue.9797, pp.669-696, 2001.

D. W. Stroock, Partial differential equations for probabilists, volume 112 of Cambridge Studies in Advanced Math, 2008.

]. Svr05, M. Sturm, and . Von-renesse, Transport inequalities, gradient estimates, entropy and Ricci curvature, Comm. Pure Appl. Math, vol.68, pp.923-940, 2005.

]. C. Vil09 and . Villani, Optimal transport, Old and new, Grund. Math. Wiss, vol.338, 2009.