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Volumn 252, Issue 2, 2012, Pages 1263-1282

Large-time asymptotics for one-dimensional Dirichlet problems for Hamilton-Jacobi equations with noncoercive Hamiltonians

Author keywords

Boundary value problems; Large time behavior; Noncoercive Hamilton Jacobi equations; Viscosity solution

Indexed keywords


EID: 80655132903     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2011.10.010     Document Type: Article
Times cited : (14)

References (31)
  • 2
    • 0024705092 scopus 로고
    • A boundary value problem for the minimum-time function
    • Bardi M. A boundary value problem for the minimum-time function. SIAM J. Control Optim. 1989, 27:776-785.
    • (1989) SIAM J. Control Optim. , vol.27 , pp. 776-785
    • Bardi, M.1
  • 3
  • 4
    • 84966252497 scopus 로고
    • Hamilton-Jacobi equations with singular boundary conditions on a free boundary and applications to differential games
    • Bardi M., Soravia P. Hamilton-Jacobi equations with singular boundary conditions on a free boundary and applications to differential games. Trans. Amer. Math. Soc. 1991, 325:205-229.
    • (1991) Trans. Amer. Math. Soc. , vol.325 , pp. 205-229
    • Bardi, M.1    Soravia, P.2
  • 5
    • 34548073020 scopus 로고    scopus 로고
    • Some homogenization results for non-coercive Hamilton-Jacobi equations
    • Barles G. Some homogenization results for non-coercive Hamilton-Jacobi equations. Calc. Var. Partial Differential Equations 2007, 30:449-466.
    • (2007) Calc. Var. Partial Differential Equations , vol.30 , pp. 449-466
    • Barles, G.1
  • 6
    • 80655144036 scopus 로고    scopus 로고
    • A PDE approach to large-time asymptotics for boundary-value problems for Hamilton-Jacobi equations, Comm. Partial Differential Equations, in press.
    • G. Barles, H. Mitake, A PDE approach to large-time asymptotics for boundary-value problems for Hamilton-Jacobi equations, Comm. Partial Differential Equations, in press.
    • Barles, G.1    Mitake, H.2
  • 7
    • 33746839663 scopus 로고    scopus 로고
    • Ergodic type problems and large time behavior of unbounded solutions of Hamilton-Jacobi equations
    • Barles G., Roquejoffre J.M. Ergodic type problems and large time behavior of unbounded solutions of Hamilton-Jacobi equations. Comm. Partial Differential Equations 2006, 31:1209-1225.
    • (2006) Comm. Partial Differential Equations , vol.31 , pp. 1209-1225
    • Barles, G.1    Roquejoffre, J.M.2
  • 8
    • 0034347336 scopus 로고    scopus 로고
    • On the large time behavior of solutions of Hamilton-Jacobi equations
    • Barles G., Souganidis P.E. On the large time behavior of solutions of Hamilton-Jacobi equations. SIAM J. Math. Anal. 2000, 31:925-939.
    • (2000) SIAM J. Math. Anal. , vol.31 , pp. 925-939
    • Barles, G.1    Souganidis, P.E.2
  • 9
    • 77951258172 scopus 로고    scopus 로고
    • Ergodicity of Hamilton-Jacobi equations with a non coercive non convex Hamiltonian in R2/Z2
    • Cardaliaguet P. Ergodicity of Hamilton-Jacobi equations with a non coercive non convex Hamiltonian in R2/Z2. Ann. Inst. H. Poincaré Anal. Non Linéaire 2010, 27(3):837-856.
    • (2010) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.27 , Issue.3 , pp. 837-856
    • Cardaliaguet, P.1
  • 10
    • 33947248437 scopus 로고    scopus 로고
    • A generalized dynamical approach to the large time behavior of solutions of Hamilton-Jacobi equations
    • Davini A., Siconolfi A. A generalized dynamical approach to the large time behavior of solutions of Hamilton-Jacobi equations. SIAM J. Math. Anal. 2006, 38:478-502.
    • (2006) SIAM J. Math. Anal. , vol.38 , pp. 478-502
    • Davini, A.1    Siconolfi, A.2
  • 11
    • 0024771431 scopus 로고
    • The Hamiltonian-Jacobi-Bellman equation for time-optimal control
    • Evans L.C., James M.R. The Hamiltonian-Jacobi-Bellman equation for time-optimal control. SIAM J. Control Optim. 1989, 6:1477-1489.
    • (1989) SIAM J. Control Optim. , vol.6 , pp. 1477-1489
    • Evans, L.C.1    James, M.R.2
  • 12
    • 0032138156 scopus 로고    scopus 로고
    • Sur la convergence du semi-groupe de Lax-Oleinik
    • Fathi A. Sur la convergence du semi-groupe de Lax-Oleinik. C. R. Acad. Sci. Paris Sér. I Math. 1998, 327:267-270.
    • (1998) C. R. Acad. Sci. Paris Sér. I Math. , vol.327 , pp. 267-270
    • Fathi, A.1
  • 13
    • 33845535277 scopus 로고    scopus 로고
    • Asymptotic solutions of Hamilton-Jacobi equations in Euclidean n space
    • Fuijita Y., Ishii H., Loreti P. Asymptotic solutions of Hamilton-Jacobi equations in Euclidean n space. Indiana Univ. Math. J. 2006, 55:1671-1700.
    • (2006) Indiana Univ. Math. J. , vol.55 , pp. 1671-1700
    • Fuijita, Y.1    Ishii, H.2    Loreti, P.3
  • 14
    • 67349084449 scopus 로고    scopus 로고
    • Surface Evolution Equations, a Level Set Approach
    • Birkhäuser Verlag, Basel
    • Giga Y. Surface Evolution Equations, a Level Set Approach. Monogr. Math. 2006, vol. 99. Birkhäuser Verlag, Basel.
    • (2006) Monogr. Math. , vol.99
    • Giga, Y.1
  • 15
    • 80655131835 scopus 로고    scopus 로고
    • Singular Neumann problems and large-time behavior of solutions of noncoercive Hamilton-Jacobi equations, submitted for publication.
    • Y. Giga, Q. Liu, H. Mitake, Singular Neumann problems and large-time behavior of solutions of noncoercive Hamilton-Jacobi equations, submitted for publication.
    • Giga, Y.1    Liu, Q.2    Mitake, H.3
  • 16
    • 45849142961 scopus 로고    scopus 로고
    • Asymptotic solutions of Hamilton-Jacobi equations with semi-periodic Hamiltonians
    • Ichihara N., Ishii H. Asymptotic solutions of Hamilton-Jacobi equations with semi-periodic Hamiltonians. Comm. Partial Differential Equations 2008, 33:784-807.
    • (2008) Comm. Partial Differential Equations , vol.33 , pp. 784-807
    • Ichihara, N.1    Ishii, H.2
  • 17
    • 68349100620 scopus 로고    scopus 로고
    • The large-time behavior of solutions of Hamilton-Jacobi equations on the real line
    • Ichihara N., Ishii H. The large-time behavior of solutions of Hamilton-Jacobi equations on the real line. Methods Appl. Anal. 2008, 15:223-242.
    • (2008) Methods Appl. Anal. , vol.15 , pp. 223-242
    • Ichihara, N.1    Ishii, H.2
  • 18
    • 70349498824 scopus 로고    scopus 로고
    • Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians
    • Ichihara N., Ishii H. Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians. Arch. Ration. Mech. Anal. 2009, 194:383-419.
    • (2009) Arch. Ration. Mech. Anal. , vol.194 , pp. 383-419
    • Ichihara, N.1    Ishii, H.2
  • 19
    • 0000102848 scopus 로고
    • Uniqueness of unbounded viscosity solution of Hamilton-Jacobi equations
    • Ishii H. Uniqueness of unbounded viscosity solution of Hamilton-Jacobi equations. Indiana Univ. Math. J. 1984, 33:721-748.
    • (1984) Indiana Univ. Math. J. , vol.33 , pp. 721-748
    • Ishii, H.1
  • 20
    • 84972566521 scopus 로고
    • Perron's method for Hamilton-Jacobi equations
    • Ishii H. Perron's method for Hamilton-Jacobi equations. Duke Math. J. 1987, 55:369-384.
    • (1987) Duke Math. J. , vol.55 , pp. 369-384
    • Ishii, H.1
  • 21
    • 84968483697 scopus 로고
    • A simple, direct proof of uniqueness for solutions of the Hamilton-Jacobi equations of Eikonal type
    • Ishii H. A simple, direct proof of uniqueness for solutions of the Hamilton-Jacobi equations of Eikonal type. Proc. Amer. Math. Soc. 1987, 100:247-251.
    • (1987) Proc. Amer. Math. Soc. , vol.100 , pp. 247-251
    • Ishii, H.1
  • 22
    • 40049091116 scopus 로고    scopus 로고
    • Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean n space
    • Ishii H. Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean n space. Ann. Inst. H. Poincaré Anal. Non Linéaire 2008, 25:231-266.
    • (2008) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.25 , pp. 231-266
    • Ishii, H.1
  • 23
    • 80655141357 scopus 로고    scopus 로고
    • Long-time asymptotic solutions of convex Hamilton-Jacobi equations with Neumann type boundary conditions
    • Partial Differential Equations, in press.
    • H. Ishii, Long-time asymptotic solutions of convex Hamilton-Jacobi equations with Neumann type boundary conditions, Calc. Var. Partial Differential Equations, in press.
    • Calc. Var.
    • Ishii, H.1
  • 24
    • 0000104617 scopus 로고
    • Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints
    • 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.
    • (1989) Math. Ann. , vol.283 , pp. 583-630
    • Lasry, J.M.1    Lions, P.L.2
  • 26
    • 54949120627 scopus 로고    scopus 로고
    • Asymptotic solutions of Hamilton-Jacobi equations with state constraints
    • Mitake H. Asymptotic solutions of Hamilton-Jacobi equations with state constraints. Appl. Math. Optim. 2008, 58:393-410.
    • (2008) Appl. Math. Optim. , vol.58 , pp. 393-410
    • Mitake, H.1
  • 27
    • 55749102303 scopus 로고    scopus 로고
    • The large-time behavior of solutions of the Cauchy-Dirichlet problem for Hamilton-Jacobi equations
    • Mitake H. The large-time behavior of solutions of the Cauchy-Dirichlet problem for Hamilton-Jacobi equations. NoDEA Nonlinear Differential Equations Appl. 2008, 15:347-362.
    • (2008) NoDEA Nonlinear Differential Equations Appl. , vol.15 , pp. 347-362
    • Mitake, H.1
  • 28
    • 68349086917 scopus 로고    scopus 로고
    • Large time behavior of solutions of Hamilton-Jacobi equations with periodic boundary data
    • Mitake H. Large time behavior of solutions of Hamilton-Jacobi equations with periodic boundary data. Nonlinear Anal. 2009, 71:5392-5405.
    • (2009) Nonlinear Anal. , vol.71 , pp. 5392-5405
    • Mitake, H.1
  • 29
    • 0033475055 scopus 로고    scopus 로고
    • Remarks on the long time behavior of the solutions of Hamilton-Jacobi equations
    • Namah G., Roquejoffre J.M. Remarks on the long time behavior of the solutions of Hamilton-Jacobi equations. Comm. Partial Differential Equations 1999, 24:883-893.
    • (1999) Comm. Partial Differential Equations , vol.24 , pp. 883-893
    • Namah, G.1    Roquejoffre, J.M.2
  • 30
    • 0035216389 scopus 로고    scopus 로고
    • Convergence to steady states or periodic solutions in a class of Hamilton-Jacobi equations
    • Roquejoffre J.M. Convergence to steady states or periodic solutions in a class of Hamilton-Jacobi equations. J. Math. Pures Appl. 2001, 80:85-104.
    • (2001) J. Math. Pures Appl. , vol.80 , pp. 85-104
    • Roquejoffre, J.M.1
  • 31
    • 53349120667 scopus 로고    scopus 로고
    • A microscopic time scale approximation to the behavior of the local slope on the faceted surface under a nonuniformity in supersaturation
    • Yokoyama E., Giga Y., Rybka P. A microscopic time scale approximation to the behavior of the local slope on the faceted surface under a nonuniformity in supersaturation. Phys. D 2008, 237:2845-2855.
    • (2008) Phys. D , vol.237 , pp. 2845-2855
    • Yokoyama, E.1    Giga, Y.2    Rybka, P.3


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