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Vanishing viscosity limits for space-time periodic Hamilton-Jacobi equations
1. | Instituto de Matemáticas, Universidad Nacional Autónoma de México, México DF 04510, Mexico, Mexico |
References:
[1] |
N. Anantharaman, R. Iturriaga, P. Padilla and H. Sánchez-Morgado, Physical solutions of the Hamilton-Jacobi equation, Disc. Cont. Dyn. Sys. Series B, 5 (2005), 513-528.
doi: 10.3934/dcdsb.2005.5.513. |
[2] |
M. Bardi, I. Capuzzo Dolcetta, "Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations,'' Birkhausser, 1997. |
[3] |
G. Barles, "Solutions de viscosité des équations de Hamilton Jacobi,'' Mathématiques et Applications 17, Springer-Verlag, 1994. |
[4] |
G. Barles and P. E. Souganidis, Space-time periodic solutions and long-time behavior of solutions to quasi-linear parabolic equations, SIAM J. Math. Anal., 32 (2001), 1311-1323.
doi: 10.1137/S0036141000369344. |
[5] |
P. Bernard, Smooth critical subsolutions of the Hamilton-Jacobi equation, Math. Res. Lett., 14 (2007), 503-511. |
[6] |
P. Bernard, Connecting orbits of time dependent Lagrangian systems, Ann. Inst. Fourier, Grenoble, 52 (2002), 1533-1568.
doi: 10.5802/aif.1924. |
[7] |
U. Bessi, Aubry-Mather theory and Hamilton-Jacobi equations, Comm. Math. Phys., 235 (2003), 495-511.
doi: 10.1007/s00220-002-0781-5. |
[8] |
G. Contreras and R. Iturriaga, Convex Hamiltonians without conjugate points, Erg. Th. Dynam. Sys., 19 (1999), 901-952.
doi: 10.1017/S014338579913387X. |
[9] |
G. Contreras, R. Iturriaga and H. Sánchez-Morgado, Weak solutions of the Hamilton Jacobi equation for Time Periodic Lagrangians, http://www.matem.unam.mx/hector/wham.pdf, Preprint. |
[10] |
M. G. Crandall, L. C. Evans and P.-L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 282 (1984), 487-502.
doi: 10.1090/S0002-9947-1984-0732102-X. |
[11] |
L. C. Evans, "Partial Differential Equations,'' Graduate Studies in Mathematics 19, AMS, 1997. |
[12] |
A. Fathi, "Weak KAM Theorem in Lagrangian Dynamics,'' To appear in Cambridge Studies in Advanced Mathematics. |
[13] |
A. Fathi, On existence of smooth critical subsolutions of the Hamilton-Jacobi equation, Pub. Mat. Uruguay, 12 (2011), 87-98. |
[14] |
W. Fleming and M. Soner, "Controlled Markov Processes and Viscosity Solutions,'' Springer 1993. |
[15] |
M. I. Freidlin and A. D. Wentzell, "Random Perturbations of Dynamical Systems,'' Springer 1998. |
[16] |
H. R. Jauslin, H. O. Kreiss and J. Moser, On the forced Burgers equation with periodic boundary conditions, "Differential Equations, La Pietra,'' Proc. of Symp. Pure Math., 65 (1996), 133-153. |
[17] |
D. Massart, Subsolution of time-periodic Hamilton-Jacobi equations, Erg. Th. Dynam. Sys., 27 (2007), 1253-1265.
doi: 10.1017/S0143385707000089. |
[18] |
T. Rockafellar, "Convex Analysis,'' Princeton University Press, 1972. |
show all references
References:
[1] |
N. Anantharaman, R. Iturriaga, P. Padilla and H. Sánchez-Morgado, Physical solutions of the Hamilton-Jacobi equation, Disc. Cont. Dyn. Sys. Series B, 5 (2005), 513-528.
doi: 10.3934/dcdsb.2005.5.513. |
[2] |
M. Bardi, I. Capuzzo Dolcetta, "Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations,'' Birkhausser, 1997. |
[3] |
G. Barles, "Solutions de viscosité des équations de Hamilton Jacobi,'' Mathématiques et Applications 17, Springer-Verlag, 1994. |
[4] |
G. Barles and P. E. Souganidis, Space-time periodic solutions and long-time behavior of solutions to quasi-linear parabolic equations, SIAM J. Math. Anal., 32 (2001), 1311-1323.
doi: 10.1137/S0036141000369344. |
[5] |
P. Bernard, Smooth critical subsolutions of the Hamilton-Jacobi equation, Math. Res. Lett., 14 (2007), 503-511. |
[6] |
P. Bernard, Connecting orbits of time dependent Lagrangian systems, Ann. Inst. Fourier, Grenoble, 52 (2002), 1533-1568.
doi: 10.5802/aif.1924. |
[7] |
U. Bessi, Aubry-Mather theory and Hamilton-Jacobi equations, Comm. Math. Phys., 235 (2003), 495-511.
doi: 10.1007/s00220-002-0781-5. |
[8] |
G. Contreras and R. Iturriaga, Convex Hamiltonians without conjugate points, Erg. Th. Dynam. Sys., 19 (1999), 901-952.
doi: 10.1017/S014338579913387X. |
[9] |
G. Contreras, R. Iturriaga and H. Sánchez-Morgado, Weak solutions of the Hamilton Jacobi equation for Time Periodic Lagrangians, http://www.matem.unam.mx/hector/wham.pdf, Preprint. |
[10] |
M. G. Crandall, L. C. Evans and P.-L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 282 (1984), 487-502.
doi: 10.1090/S0002-9947-1984-0732102-X. |
[11] |
L. C. Evans, "Partial Differential Equations,'' Graduate Studies in Mathematics 19, AMS, 1997. |
[12] |
A. Fathi, "Weak KAM Theorem in Lagrangian Dynamics,'' To appear in Cambridge Studies in Advanced Mathematics. |
[13] |
A. Fathi, On existence of smooth critical subsolutions of the Hamilton-Jacobi equation, Pub. Mat. Uruguay, 12 (2011), 87-98. |
[14] |
W. Fleming and M. Soner, "Controlled Markov Processes and Viscosity Solutions,'' Springer 1993. |
[15] |
M. I. Freidlin and A. D. Wentzell, "Random Perturbations of Dynamical Systems,'' Springer 1998. |
[16] |
H. R. Jauslin, H. O. Kreiss and J. Moser, On the forced Burgers equation with periodic boundary conditions, "Differential Equations, La Pietra,'' Proc. of Symp. Pure Math., 65 (1996), 133-153. |
[17] |
D. Massart, Subsolution of time-periodic Hamilton-Jacobi equations, Erg. Th. Dynam. Sys., 27 (2007), 1253-1265.
doi: 10.1017/S0143385707000089. |
[18] |
T. Rockafellar, "Convex Analysis,'' Princeton University Press, 1972. |
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