Asymptotic solutions for large time of Hamilton–Jacobi equations in euclidean n space
Annales de l'I.H.P. Analyse non linéaire (2008)
- Volume: 25, Issue: 2, page 231-266
- ISSN: 0294-1449
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topIshii, Hitoshi. "Asymptotic solutions for large time of Hamilton–Jacobi equations in euclidean n space." Annales de l'I.H.P. Analyse non linéaire 25.2 (2008): 231-266. <http://eudml.org/doc/78787>.
@article{Ishii2008,
author = {Ishii, Hitoshi},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {weak KAM theory; convexity assumptions; unique viscosity solution},
language = {eng},
number = {2},
pages = {231-266},
publisher = {Elsevier},
title = {Asymptotic solutions for large time of Hamilton–Jacobi equations in euclidean n space},
url = {http://eudml.org/doc/78787},
volume = {25},
year = {2008},
}
TY - JOUR
AU - Ishii, Hitoshi
TI - Asymptotic solutions for large time of Hamilton–Jacobi equations in euclidean n space
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2008
PB - Elsevier
VL - 25
IS - 2
SP - 231
EP - 266
LA - eng
KW - weak KAM theory; convexity assumptions; unique viscosity solution
UR - http://eudml.org/doc/78787
ER -
References
top- [1] Alvarez O., Bounded-from-below viscosity solutions of Hamilton–Jacobi equations, Differential Integral Equations10 (3) (1997) 419-436. Zbl0890.35026MR1744854
- [2] Aubin J.-P., Cellina A., Differential Inclusions. Set-Valued Maps and Viability Theory, Grundlehren der Mathematischen Wissenschaften, vol. 264, Springer-Verlag, Berlin, 1984. Zbl0538.34007MR755330
- [3] Barles G., Solutions de viscosité des équations de Hamilton–Jacobi, Mathématiques & Applications (Berlin), vol. 17, Springer-Verlag, Paris, 1994. Zbl0819.35002MR1613876
- [4] Bardi M., Capuzzo-Dolcetta I., Optimal Control and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations, Systems & Control: Foundations & Applications, Birkhäuser Boston, Boston, MA, 1997, With appendices by Maurizio Falcone and Pierpaolo Soravia. Zbl0890.49011
- [5] Barles G., Roquejoffre J.-M., Ergodic type problems and large time behaviour of unbounded solutions of Hamilton–Jacobi equations, Comm. Partial Differential Equations31 (8) (2006) 1209-1225. Zbl1107.35019MR2254612
- [6] Barles G., Souganidis P.E., On the large time behavior of solutions of Hamilton–Jacobi equations, SIAM J. Math. Anal.31 (4) (2000) 925-939. Zbl0960.70015MR1752423
- [7] Barles G., 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. Zbl0986.35047MR1856250
- [8] Barron E.N., Jensen R., Semicontinuous viscosity solutions for Hamilton–Jacobi equations with convex Hamiltonians, Comm. Partial Differential Equations15 (12) (1990) 1713-1742. Zbl0732.35014MR1080619
- [9] Barron E.N., Jensen R., Optimal control and semicontinuous viscosity solutions, Proc. Amer. Math. Soc.113 (2) (1991) 397-402. Zbl0741.49010MR1076572
- [10] Clarke F.H., Optimization and Nonsmooth Analysis, SIAM, Philadelphia, 1983. Zbl0696.49002MR709590
- [11] Crandall M.G., Ishii H., Lions P.-L., User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc.27 (1992) 1-67. Zbl0755.35015MR1118699
- [12] Davini A., Siconolfi A., A generalized dynamical approach to the large time behavior of solutions of Hamilton–Jacobi equations, SIAM J. Math. Anal.38 (2) (2006) 478-502. Zbl1109.49034MR2237158
- [13] Fathi A., Théorème KAM faible et théorie de Mather pour les systèmes lagrangiens, C. R. Acad. Sci. Paris Sér. I Math.324 (9) (1997) 1043-1046. Zbl0885.58022MR1451248
- [14] Fathi A., Sur la convergence du semi-groupe de Lax–Oleinik, C. R. Acad. Sci. Paris Sér. I Math.327 (3) (1998) 267-270. Zbl1052.37514MR1650261
- [15] A. Fathi, Weak KAM theorem in Lagrangian dynamics, in press. Zbl0885.58022
- [16] Fathi A., Siconolfi A., Existence of critical subsolutions of the Hamilton–Jacobi equation, Invent. Math.155 (2) (2004) 363-388. Zbl1061.58008MR2031431
- [17] Fathi A., Siconolfi A., PDE aspects of Aubry–Mather theory for quasiconvex Hamiltonians, Calc. Var. Partial Differential Equations22 (2) (2005) 185-228. Zbl1065.35092MR2106767
- [18] Fujita Y., Ishii H., Loreti P., Asymptotic solutions of viscous Hamilton–Jacobi equations with Ornstein–Uhlenbeck operator, Comm. Partial Differential Equations31 (6) (2006) 827-848. Zbl1101.35017MR2233043
- [19] Y. Fujita, H. Ishii, P. Loreti, Asymptotic solutions of Hamilton–Jacobi equations in Euclidean n space, Indiana Univ. Math. J., in press. Zbl1112.35041MR2270933
- [20] N. Ichihara, H. Ishii, in preparation.
- [21] Ishii H., A generalization of a theorem of Barron and Jensen and a comparison theorem for lower semicontinuous viscosity solutions, Proc. Roy. Soc. Edinburgh Sect. A131 (1) (2001) 137-154. Zbl1158.49302MR1820297
- [22] H. Ishii, H. Mitake, Representation formulas for solutions of Hamilton–Jacobi equations, preprint. Zbl1136.35016
- [23] Lions P.-L., Generalized Solutions of Hamilton–Jacobi Equations, Research Notes in Mathematics, vol. 69, Pitman (Advanced Publishing Program), Boston, MA, 1982. Zbl0497.35001MR667669
- [24] P.-L. Lions, G. Papanicolaou, S. Varadhan, Homogenization of Hamilton–Jacobi equations, unpublished preprint.
- [25] Namah G., Roquejoffre J.-M., Remarks on the long time behaviour of the solutions of Hamilton–Jacobi equations, Comm. Partial Differential Equations24 (5–6) (1999) 883-893. Zbl0924.35028MR1680905
- [26] Rockafellar T., Convex Analysis, Princeton University Press, Princeton, 1970. Zbl0193.18401MR274683
- [27] Roquejoffre J.-M., Convergence to steady states or periodic solutions in a class of Hamilton–Jacobi equations, J. Math. Pures Appl.(9) 80 (1) (2001) 85-104. Zbl0979.35033MR1810510
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