On the large time behavior of solutions of the Dirichlet problem for subquadratic viscous Hamilton-Jacobi equations

Journal des Mathematiques Pures et Appliquees

Volumn 94, Issue 5, 2010, Pages 497-519

  Barles, Guy ^a   Porretta, Alessio ^b   Tchamba, Thierry Tabet ^a,c  

^a UNIVERSITÉ DE TOURS   (France)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

^c UNIVERSITY OF YAOUNDÉ I   (Cameroon)

Author keywords

Dirichlet problem; Ergodic problem; Large time behavior; Subquadratic case; Viscosity solutions; Viscous Hamilton Jacobi Equations

Indexed keywords

EID: 77957785772     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2010.03.006     Document Type: Article

References (15)

1. Barles G. Interior gradient bounds for the mean curvature equation by viscosity solution approach. Differential Integral Equations 1991, 4(2):263-275.
2. Barles G., Biton S., Ley O. A geometrical approach to the study of unbounded solutions of quasilinear parabolic equations. Arch. Ration. Mech. Anal. 2002, 162(4):287-325.
3. Barles G., Da Lio F. On generalized Dirichlet problem for viscous Hamilton-Jacobi equations. J. Math. Pures Appl. 2004, 83:53-75.
4. α estimates for viscosity solutions of Neumann-type boundary value problems. J. Differential Equations 2006, 225:202-241.
5. Barles G., Souganidis P.E. Space-time periodic solutions and long-time behavior of solutions to quasi-linear parabolic equations. SIAM J. Math. Anal. 2001, 32(6):1311-1323.
6. Crandall M.G., Ishii H., Lions P.-L. User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 1992, 27(1):1-67.
7. Da Lio F. Comparison results for quasilinear equations in annular domains and applications. Comm. Partial Differential Equations 2002, 27(1-2):283-323.
8. Da Lio F. Large time behavior of solutions to parabolic equation with Neumann boundary conditions. J. Math. Anal. Appl. 2008, 339:384-398.
9. Ishii H. Perron's Method for Hamilton-Jacobi equations. Duke Math. J. 1987, 55(2):369-384.
10. Ishii H., Lions P.-L. Viscosity solutions of fully nonlinear second-order elliptic PDE's. J. Differential Equations 1990, 83(1):26-78.
11. Gilbarg D., Trudinger N.S. Elliptic Partial Differential Equations of Second Order 1983, Springer-Verlag.
12. Lasry J.-M., Lions P.-L. Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints. Math. Ann. 1989, 283:583-630.
13. Porretta A., Veron L. Asymptotic behaviour of the gradient of large solution to some nonlinear elliptic equations. Adv. Nonlinear Stud. 2006, 6:351-378.
14. Souplet P., Zhang Qi S. Global solutions of inhomogenous Hamilton-Jacobi equations. J. Anal. Math. 2006, 99:355-396.
15. T. Tabet Tchamba, Large time behavior of solutions of viscous Hamilton-Jacobi equations with superquadratic Hamiltonian, Asymptot. Anal., in press.