J. M. Arrieta, A. Rodriguez-bernal, and P. Souplet, Boundedness of global solutions for nonlinear parabolic equations involving gradient blow-up phenomena, Ann. Sc. Norm. Super. Pisa Cl. Sci, vol.5, issue.3, pp.1-15, 2004.

M. Bardi and I. Capuzzo-dolcetta, Optimal Control and Viscosity Solutions of Hamilton- Jacobi-Bellman Equations, Systems Control Found, Appl, 1997.

G. Barles, Solutions de Viscosité des Equations d'Hamilton-Jacobi, Mathématiques & Applications, vol.17, 1994.

G. Barles and J. Busca, EXISTENCE AND COMPARISON RESULTS FOR FULLY NONLINEAR DEGENERATE ELLIPTIC EQUATIONS WITHOUT ZEROTH-ORDER TERM1*, Communications in Partial Differential Equations, vol.26, issue.11-12, pp.2323-2337, 2001.
DOI : 10.1081/PDE-100107824

G. Barles and F. Da-lio, On the generalized Dirichlet problem for viscous Hamilton???Jacobi equations, Journal de Math??matiques Pures et Appliqu??es, vol.83, issue.1, pp.53-75, 2004.
DOI : 10.1016/S0021-7824(03)00070-9

G. Barles, G. Díaz, and J. I. Díaz, Uniqueness and continuum of foliated solutions for a quasilinear elliptic equation with a non lipschitz nonlinearity, Communications in Partial Differential Equations, vol.1, issue.5-6, pp.1037-1050, 1992.
DOI : 10.1007/BF02792551

G. Barles and B. Perthame, Exit Time Problems in Optimal Control and Vanishing Viscosity Method, SIAM Journal on Control and Optimization, vol.26, issue.5, pp.1133-1148, 1988.
DOI : 10.1137/0326063

G. Barles and P. E. Souganidis, On the large time behaviour of solutions of Hamilton- Jacobi equations, SIAM J. Math. Anal, pp.31-925, 2000.

S. Benachour, S. Hapca, and P. , Laurençot, Decay estimates for a viscous Hamilton-Jacobi equation with homogeneous Dirichlet boundary conditions, Asymptot. Anal, vol.51, pp.209-229, 2007.

M. G. Crandall, H. Ishii, and P. Lions, user's guide to viscosity solutions\\ of second order\\ partial differential equations, Bulletin of the American Mathematical Society, vol.27, issue.1, pp.1-67, 1992.
DOI : 10.1090/S0273-0979-1992-00266-5

Y. Giga, S. Goto, H. Ishii, and M. Sato, Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains, Math. J, pp.40-443, 1991.

B. H. Gilding, M. Guedda, and R. Kersner, The Cauchy problem for ut=??u+|???u|q, Journal of Mathematical Analysis and Applications, vol.284, issue.2, pp.733-755, 2003.
DOI : 10.1016/S0022-247X(03)00395-0

O. A. Lady?enskaja, V. A. Solonnikov, and N. N. , Ural'ceva, Linear and Quasi-linear Equations of Parabolic Type, Amer. Math. Soc, 1968.

. Ph and . Laurençot, Convergence to steady states for a one-dimensional viscous Hamilton- Jacobi equation with Dirichlet boundary conditions, Pacific J. Math, vol.230, pp.347-364, 2007.

G. Namah and J. Roquejoffre, Remarks on the long time behaviour of the solutions of hamilton-jacobi equations, Communications in Partial Differential Equations, vol.12, issue.5-6, pp.883-893, 1999.
DOI : 10.1007/s000300050029

J. Roquejoffre, Convergence to steady states or periodic solutions in a class of Hamilton???Jacobi equations, Journal de Math??matiques Pures et Appliqu??es, vol.80, issue.1, pp.85-104, 2001.
DOI : 10.1016/S0021-7824(00)01183-1

. Ph and . Souplet, Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions, Differential Integral Equations, vol.15, pp.237-256, 2002.

. Ph, Q. S. Souplet, and . Zhang, Global solutions of inhomogeneous Hamilton-Jacobi equations, J. Analyse Math, vol.99, pp.355-396, 2006.

C. Stinner, Convergence to steady states in a viscous Hamilton???Jacobi equation with degenerate diffusion, Journal of Differential Equations, vol.248, issue.2, p.preprint, 2009.
DOI : 10.1016/j.jde.2009.09.019

T. and T. Tchamba, Large time behavior of solutions of viscous Hamilton-Jacobi equations with superquadratic Hamiltonian, p.preprint, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00371068

T. I. Zelenyak, Stabilization of solutions of boundary value problems for a second order parabolic equation with one space variable, Differential Equations, vol.4, pp.17-22, 1968.