A. Ajdari, Course 2 : Mechanical Aging and Non-linear Rheology of Concentrated Colloidal Suspensions : Experimental Facts and Simple Models, Slow Relaxations and nonequilibrium dynamics in condensed matter, pp.41-73, 2003.

[. Bardet, A. Christen, A. Guillin, F. Malrieu, and P. Zitt, Total variation estimates for the TCP process Heterogeneities in amorphous systems under shear, Dynamical Heterogeneities in Glasses, Colloids, and Granular Media, 2011.

D. [. Behr, O. Arora, M. Coronado-matutti, and . Pasquali, Stabilized Finite Element Methods of GLS Type for Oldroyd-B Viscoelastic Fluid, European Congress on Computational Methods in Applied Science and Engineering ECCO- MAS, 2004.

K. [. Bellman and . Cooke, Differential-difference equations, 1963.

[. B. Alaya and B. Jourdain, Probabilistic Approximation of a Nonlinear Parabolic Equation Occurring in Rheology, Journal of Applied Probability, vol.38, issue.02, pp.528-546, 2007.
DOI : 10.1007/BF00960074

L. [. Benoit, C. L. He, T. Bris, and . Lelièvre, MATHEMATICAL ANALYSIS OF A ONE-DIMENSIONAL MODEL FOR AN AGING FLUID, Mathematical Models and Methods in Applied Sciences, vol.23, issue.09, pp.1561-1602, 2013.
DOI : 10.1142/S0218202513500164

URL : https://hal.archives-ouvertes.fr/hal-00676678

]. D. Benon and . Benoit, Various theoretical and numerical issues related to the simulation of non- Newtonian fluids

C. [. Bird, R. Curtiss, O. Armstrong, and . Hassager, Dynamics of Polymeric Liquids , 2 Volume Set. Dynamics of Polymeric Liquids, 1991.

A. [. Bocquet, A. Colin, and . Ajdari, Kinetic Theory of Plastic Flow in Soft Glassy Materials, Physical Review Letters, vol.103, issue.3, p.36001, 2009.
DOI : 10.1103/PhysRevLett.103.036001

T. [. Boyaval, C. Lelièvre, and . Mangoubi, Free-energy-dissipative schemes for the Oldroyd-B model. Mathematical Modelling and Numerical Analysis, pp.523-561, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00204620

I. [. Cancès, Y. Catto, and . Gati, Mathematical Analysis of a Nonlinear Parabolic Equation Arising in the Modelling of Non-Newtonian Flows, SIAM Journal on Mathematical Analysis, vol.37, issue.1, pp.60-82, 2005.
DOI : 10.1137/S0036141003430044

C. [. Cancès and . Bris, Convergence to equilibrium of a multiscale model for suspensions. Discrete Contin, Dyn. Syst. Ser. B, vol.6, issue.3, pp.449-470, 2006.

I. [. Cancès, Y. Catto, C. L. Gati, and . Bris, Well-Posedness of a Multiscale Model for Concentrated Suspensions, Multiscale Modeling & Simulation, vol.4, issue.4, pp.1041-1058, 2005.
DOI : 10.1137/040621223

]. H. Car67 and . Cartan, Calcul différentiel, 1967.

A. [. Derec, F. Ajdari, and . Lequeux, Rheology and aging: A simple approach, The European Physical Journal E, vol.4, issue.3, pp.355-361, 2001.
DOI : 10.1007/s101890170118

]. Y. Gat05 and . Gati, Numerical simulation of a micro?macro model of concentrated suspensions. International journal for numerical methods in fluids, pp.8-9, 2005.

]. J. Goy08 and . Goyon, Matériaux amorphes : des solides qui coulent de façon collective, 2008.

. Gth-+-06-]-b, L. Gueslin, B. Talini, Y. Herzhaft, C. Peysson et al., Flow induced by a sphere settling in an aging yield-stress fluid, Physics of Fluids, vol.18, p.103101, 2006.

J. [. Guillopé and . Saut, Global Existence and One-dimensional Nonlinear Stability of Shearing Motions of Viscoelastic Fluids of Oldroyd Type. RAIRO- Mathematical Modelling and Numerical Analysis, pp.369-401, 1990.

S. [. Hale and . Lunel, Introduction to Functional Differential Equations, Applied Mathematical Sciences, 1993.
DOI : 10.1007/978-1-4612-4342-7

L. [. He and . Xu, Global Well-Posedness for Viscoelastic Fluid System in Bounded Domains, SIAM Journal on Mathematical Analysis, vol.42, issue.6, p.2610, 2010.
DOI : 10.1137/10078503X

F. [. Hébraud and . Lequeux, Mode-Coupling Theory for the Pasty Rheology of Soft Glassy Materials, Physical Review Letters, vol.81, issue.14, pp.2934-2937, 1998.
DOI : 10.1103/PhysRevLett.81.2934

Y. [. Kawashima and . Shibata, Global existence and exponential stability of small solutions to nonlinear viscoelasticity. Communications in mathematical physics, pp.189-208, 1992.

]. R. Keu89 and . Keunings, Simulation of viscoelastic fluid flow. Fundamentals of computer modeling for polymer processing, pp.402-470, 1989.

]. R. Keu00 and . Keunings, A survey of computational rheology, Proceedings of the XIIIth International Congress on Rheology, pp.7-14, 2000.

[. Bris and T. Lelièvre, Multiscale Modelling of Complex Fluids: A Mathematical Initiation, Multiscale modeling and simulation in science, pp.49-137, 2009.
DOI : 10.1007/978-3-540-88857-4_2

URL : https://hal.archives-ouvertes.fr/inria-00165171

[. Bris and T. Lelièvre, Micro-macro models for viscoelastic fluids: modelling, mathematics and numerics, Science China Mathematics, vol.6, issue.2, pp.353-384, 2012.
DOI : 10.1007/s11425-011-4354-y

URL : https://hal.archives-ouvertes.fr/hal-00562325

]. J. Lio69 and . Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Études mathématiques. Gauthier-Villars, 1969.

]. J. Oli10 and . Olivier, Asymptotic analysis in flow curves for a model of soft glassy fluids, Zeitschrift für angewandte Mathematik und Physik, pp.445-466, 2010.

M. [. Olivier and . Renardy, Glass Transition Seen through Asymptotic Expansions, OR13] J. Olivier and M. Renardy. On the Generalization of the Hébraud?Lequeux Model to Multidimensional Flows. Archive for Rational Mechanics and Analysis, pp.1144-1167, 2011.
DOI : 10.1137/100800725

URL : https://hal.archives-ouvertes.fr/hal-00497462

]. L. Per00 and . Perko, Differential Equations and Dynamical Systems, Texts in Applied Mathematics, 2000.

]. G. Pic04, . [. Picard, A. Picard, L. Ajdari, F. Bocquet et al., Hétérogénéité de l'écoulement de fluides à seuil : approche phénoménologique et modélisation élasto-plastique Simple model for heterogeneous flows of yield stress fluids Elastic consequences of a single plastic event : A step towards the microscopic modeling of the flow of yield stress fluids, Ren00] M. Renardy. Mathematical Analysis of Viscoelastic Flows. CBMS-NSF regional conference series in applied mathematics. Society for Industrial and Applied Mathematics, pp.371-381, 2000.

]. M. Ren09a and . Renardy, Global Existence of Solutions for Shear Flow of Certain Viscoelastic Fluids, Journal of Mathematical Fluid Mechanics, vol.11, issue.1, pp.91-99, 2009.

]. M. Ren09b and . Renardy, Some Global Stability Results for Shear Flows of Viscoelastic Fluids, Journal of Mathematical Fluid Mechanics, vol.11, issue.1, pp.100-109, 2009.

]. L. Str78 and . Struik, Physical aging in amorphous polymers and other materials, 1978.

. J. Ssab99, M. Sun, R. Smith, R. Armstrong, and . Brown, Finite element method for viscoelastic flows based on the discrete adaptive viscoelastic stress splitting and the discontinuous Galerkin method : DAVSS-G/DG, Journal of Non-Newtonian Fluid Mechanics, vol.86, issue.3, pp.281-307, 1999.

]. Szn91 and . Sznitman, Topics in propagation of chaos, Ecole d'Eté de Probabilités de Saint-Flour XIX -1989, pp.165-251, 1991.

]. R. Tem79 and . Temam, Navier-Stokes equations : theory and numerical analysis, 1979.

]. M. Tsa09 and . Tsamados, Mechanical response of glassy materials : theory and simulation, 2009.