S. Adly, H. Attouch, and A. Cabot, Finite Time Stabilization of Nonlinear Oscillators Subject to dry Friction, Adv. Mech. Math, vol.12, pp.289-304, 2006.
DOI : 10.1007/0-387-29195-4_24

URL : https://hal.archives-ouvertes.fr/hal-00068295

F. Alvarez, On the Minimizing Property of a Second Order Dissipative System in Hilbert Spaces, SIAM Journal on Control and Optimization, vol.38, issue.4, pp.1102-1119, 2000.
DOI : 10.1137/S0363012998335802

F. Alvarez, Weak Convergence of a Relaxed and Inertial Hybrid Projection-Proximal Point Algorithm for Maximal Monotone Operators in Hilbert Space, SIAM Journal on Optimization, vol.14, issue.3, pp.773-782, 2004.
DOI : 10.1137/S1052623403427859

F. Alvarez and H. Attouch, An inertial proximal method for monotone operators via discretization of a nonlinear oscillator with damping, Set-Valued Analysis, vol.9, issue.1/2, pp.3-11, 2001.
DOI : 10.1023/A:1011253113155

F. Alvarez and H. Attouch, The heavy ball with friction dynamical system for convex constrained minimization problems, Optimization (Namur Lecture Notes in Econom. and Math. Systems, vol.481, pp.25-35, 1998.

F. Alvarez and H. Attouch, Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria, ESAIM: Control, Optimisation and Calculus of Variations, vol.6, pp.539-552, 2001.
DOI : 10.1051/cocv:2001100

F. Alvarez, H. Attouch, J. Bolte, and P. Redont, A second-order gradient-like dissipative dynamical system with Hessian-driven damping., Journal de Math??matiques Pures et Appliqu??es, vol.81, issue.8, pp.747-779, 2002.
DOI : 10.1016/S0021-7824(01)01253-3

A. S. Antipin, Minimization of convex functions on convex sets by means of differential equations (in Russian), Differ, Uravn. Differential Equations, vol.30, issue.309, pp.1475-1486, 1994.

H. Attouch, D. Aze, and R. Wets, Convergence of convex-concave saddle functions: Applications to convex programming and mechanics, Ann. Inst. Poincaré, vol.5, issue.6, pp.537-572, 1988.

H. Attouch, J. Bolte, P. Redont, and A. Soubeyran, Alternating proximal algorithms for weakly coupled minimization problems. Applications to dynamical games and PDE's, J. of Convex Analysis, vol.15, issue.3, pp.485-506, 2008.

H. Attouch, A. Cabot, and P. Redont, The dynamics of elastic shocks via epigraphical regularization of a differential inclusion. Barrier and penalty approximations, Adv. Math. Sci. Appl, vol.12, issue.1, pp.273-306, 2002.

H. Attouch and R. Cominetti, A Dynamical Approach to Convex Minimization Coupling Approximation with the Steepest Descent Method, Journal of Differential Equations, vol.128, issue.2, pp.519-540, 1996.
DOI : 10.1006/jdeq.1996.0104

H. Attouch and M. Czarnecki, Asymptotic Control and Stabilization of Nonlinear Oscillators with Non-isolated Equilibria, Journal of Differential Equations, vol.179, issue.1, pp.278-310, 2002.
DOI : 10.1006/jdeq.2001.4034

H. Attouch, X. Goudou, and P. Redont, THE HEAVY BALL WITH FRICTION METHOD, I. THE CONTINUOUS DYNAMICAL SYSTEM: GLOBAL EXPLORATION OF THE LOCAL MINIMA OF A REAL-VALUED FUNCTION BY ASYMPTOTIC ANALYSIS OF A DISSIPATIVE DYNAMICAL SYSTEM, Communications in Contemporary Mathematics, vol.02, issue.01, pp.1-34, 2000.
DOI : 10.1142/S0219199700000025

H. Attouch and A. Soubeyran, Inertia and reactivity in decision making as cognitive variational inequalities, J. Convex. Anal, vol.13, issue.2, pp.207-224, 2006.

J. Baillon and G. Haddad, Quelques propri??t??s des op??rateurs angle-born??s etn-cycliquement monotones, Israel Journal of Mathematics, vol.17, issue.2, pp.137-150, 1977.
DOI : 10.1007/BF03007664

J. Baillon and A. Haraux, Comportement a l'infini pour les equations d'???volution avec forcing p???riodique, Archive for Rational Mechanics and Analysis, vol.29, issue.1, pp.101-109, 1977.
DOI : 10.1007/BF00280830

J. Bolte, Continuous Gradient Projection Method in Hilbert Spaces, Journal of Optimization Theory and Applications, vol.41, issue.2, pp.235-259, 2003.
DOI : 10.1023/B:JOTA.0000005445.21095.02

J. Bolte and M. Teboulle, Barrier Operators and Associated Gradient-Like Dynamical Systems for Constrained Minimization Problems, SIAM Journal on Control and Optimization, vol.42, issue.4, pp.1266-1292, 2003.
DOI : 10.1137/S0363012902410861

H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, Mathematical Studies, 1973.

A. Cabot, Inertial Gradient-Like Dynamical System Controlled by a Stabilizing Term, Journal of Optimization Theory and Applications, vol.128, issue.2, pp.275-303, 2004.
DOI : 10.1023/B:JOTA.0000015685.21638.8d

URL : https://hal.archives-ouvertes.fr/hal-00068878

T. Cazenave and A. Haraux, An introduction to semilinear evolution equations, Oxford Lecture Series in Mathematics and its Applications 13, 1998.

P. L. Combettes and S. A. Hirstoaga, Visco-penalization of the sum of two operators, Nonlinear Analysis, TMA, vol.69, issue.2, pp.579-591, 2008.

R. Cominetti, J. Peypouquet, and S. Sorin, Strong asymptotic convergence of evolution equations governed by maximal monotone operators with Tikhonov regularization, Journal of Differential Equations, vol.245, issue.12, pp.3753-3763, 2008.
DOI : 10.1016/j.jde.2008.08.007

S. Ervedoza and E. Zuazua, Uniformly exponentially stable approximations for a class of damped systems, Journal de Math??matiques Pures et Appliqu??es, vol.91, issue.1, pp.20-48, 2009.
DOI : 10.1016/j.matpur.2008.09.002

URL : https://hal.archives-ouvertes.fr/hal-00681693

S. D. Flam and J. Morgan, NEWTONIAN MECHANICS AND NASH PLAY, International Game Theory Review, vol.06, issue.02, pp.181-194, 2004.
DOI : 10.1142/S0219198904000149

I. Gallagher, Asymptotic of the Solutions of Hyperbolic Equations with a Skew-Symmetric Perturbation, Journal of Differential Equations, vol.150, issue.2, pp.363-384, 1998.
DOI : 10.1006/jdeq.1998.3487

J. K. Hale and G. , Convergence in gradient-like systems with applications to PDE, ZAMP Zeitschrift f???r angewandte Mathematik und Physik, vol.4, issue.2, pp.63-125, 1992.
DOI : 10.1007/BF00944741

A. Haraux, Systèmes dynamiques dissipatifs et applications, 1991.

J. Hofbauer and S. Sorin, Best response dynamics for continuous zero-sum games, Discrete and Continuous Dynamical Systems, pp.215-224, 2006.

P. E. Maingé, Regularized and inertial algorithms for common fixed points of nonlinear operators, Journal of Mathematical Analysis and Applications, vol.344, issue.2, pp.876-887, 2008.
DOI : 10.1016/j.jmaa.2008.03.028

D. Monderer, L. S. Shapley, and P. Games, Potential Games, Games and Economic Behavior, vol.14, issue.1, pp.124-143, 1996.
DOI : 10.1006/game.1996.0044

Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bulletin of the American Mathematical Society, vol.73, issue.4, pp.591-597, 1967.
DOI : 10.1090/S0002-9904-1967-11761-0

B. T. Polyak, Introduction to Optimization, Optimization Software, 1987.

R. T. Rockafellar, Monotone operators associated with saddle-functions and mini-max problems , in Nonlinear Functional Analysis, Proceedings of Symposia in Pure Mathematics, pp.241-250, 1976.

M. Schatzman, A class of nonlinear differential equations of second order in time, Nonlinear Analysis: Theory, Methods & Applications, vol.2, issue.3, pp.355-373, 1978.
DOI : 10.1016/0362-546X(78)90022-6

URL : https://hal.archives-ouvertes.fr/hal-01294058