Large time behavior of solutions to parabolic equations with Neumann boundary conditions

Journal of Mathematical Analysis and Applications

Volumn 339, Issue 1, 2008, Pages 384-398

  Da Lio, Francesca ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

Asymptotic behavior; Boundary value problems for parabolic PDEs; Ergodic problems; Viscosity solutions

Indexed keywords

EID: 35248852825     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.06.052     Document Type: Article

References (28)

1. Barles G. Interior gradient bounds for the mean curvature equation by viscosity solutions methods. Differential Integral Equations 4 2 (1991) 263-275
2. Barles G. Nonlinear Neumann boundary conditions for quasilinear degenerate elliptic equations and applications. J. Differential Equations 154 (1999) 191-224
3. Barles G., Biton S., and Ley O. A geometrical approach to the study of unbounded solutions of quasilinear parabolic equations. Arch. Ration. Mech. Anal. 162 4 (2002) 287-325
4. Barles G., and Da Lio F. On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions. Ann. Inst. H. Poincaré Anal. Non Linèaire 22 5 (2005) 521-541
5. 0, α estimates for viscosity solutions of Neumann-type boundary value problems. J. Differential Equations 225 1 (2006) 202-241
6. Barles G., and Perthame B. Exit time problems in optimal control and vanishing viscosity method. SIAM J. Control Optim. 26 5 (1988) 1133-1148
7. Barles G., and Roquejoffre J.M. Ergodic type problems and large time behaviour of unbounded solutions of Hamilton-Jacobi equations. Comm. Partial Differential Equations 31 7-9 (2006) 1209-1225
8. Barles G., and Souganidis P.E. On the large time behaviour of solutions of Hamilton-Jacobi equations. SIAM J. Math. Anal. 31 4 (2000) 925-939
9. Barles G., and Souganidis P.E. Space-time periodic solutions and long-time behavior of solutions to quasi-linear parabolic equations. SIAM J. Math. Anal. 32 6 (2001) 1311-1323
10. 1, β regularity of viscosity solutions via a continuous-dependence result. Adv. Differential Equations 9 3-4 (2004) 447-480
11. Caffarelli L., and Cabre X. Fully Nonlinear Elliptic Equations. Amer. Math. Soc. Colloq. Publ. vol. 43 (1995), Amer. Math. Soc.
12. Crandall M.G., Ishii H., and Lions P.L. User's guide to viscosity solutions of second order Partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1-67
13. p-theory for fully nonlinear uniformly parabolic equations. Comm. Partial Differential Equations 25 11-12 (2000) 1997-2053
14. Da Lio F. Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations. Comm. Pure Appl. Anal. 3 3 (2004) 395-415
15. Da Lio F., and Sirakov B. Symmetry properties of viscosity solutions to nonlinear uniformly elliptic equations. J. Eur. Math. Soc. 9 (2007) 317-330
16. Evans L.C. The perturbed test function method for viscosity solutions of nonlinear PDE. Proc. Roy. Soc. Edinburgh Sect. A 111 3-4 (1989) 359-375
17. Evans L.C. Periodic homogenisation of certain fully nonlinear partial differential equations. Proc. Roy. Soc. Edinburgh Sect. A 120 3-4 (1992) 245-265
18. Fathi A. Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens. C. R. Math. Acad. Sci. Paris Sér. I 324 (1997) 1043-1046
19. Fathi A. Solutions KAM faibles conjuguées et barrières de Peierls. C. R. Math. Acad. Sci. Paris Sér. I 325 6 (1997) 649-652
20. Fathi A. Sur la convergence du semi-groupe de Lax-Oleinik. C. R. Math. Acad. Sci. Paris Sér. I 327 3 (1998) 267-270
21. A. Fathi, Maderna, Weak KAM theorem on non compact manifolds, preprint
22. Ishii H. Almost periodic homogenization of Hamilton-Jacobi equations. International Conference on Differential Equations, vols. 1, 2. Berlin, 1999 (2000), World Sci. Publishing, River Edge, NJ 600-605
23. Fujita Y., Ishii H., and Loreti P. Asymptotic solutions to Hamilton-Jacobi equations in Euclidean n space. Indiana Univ. Math. J. 55 5 (2006) 1671-1700
24. Ishii H., and Lions P.L. Viscosity solutions of fully nonlinear second-order elliptic partial differential equations. J. Differential Equations 83 1 (1990) 26-78
25. P.-L. Lions, G. Papanicolaou, S.R. S Varadhan, unpublished preprint
26. Namah G., and Roquejoffre J.-M. Remarks on the long time behaviour of the solutions of Hamilton-Jacobi equations. Comm. Partial Differential Equations 24 5-6 (1999) 883-893
27. Pucci C. Operatori ellittici estremanti. Ann. Mat. Pura Appl. 72 (1966) 141-170
28. Wang L. On the regularity theory of fully nonlinear parabolic equations. I. Comm. Pure Appl. Math. 45 (1992) 27-76