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Volumn 56, Issue 9, 2006, Pages 1238-1254

An approximation scheme for the effective Hamiltonian and applications

Author keywords

Effective Hamiltonian; Eikonal equation; Hamilton Jacobi equations; Hamiltonian systems; Semi Lagrangian approximation

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; MATHEMATICAL OPERATORS; NUMERICAL ANALYSIS; PROBLEM SOLVING;

EID: 33745573399     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2006.03.006     Document Type: Article
Times cited : (17)

References (29)
  • 1
    • 0003267441 scopus 로고
    • Solutions de viscosité des equations de Hamilton-Jacobi
    • Springer, Berlin
    • Barles G. Solutions de viscosité des equations de Hamilton-Jacobi. Mathematics and Applications (1994), Springer, Berlin
    • (1994) Mathematics and Applications
    • Barles, G.1
  • 2
    • 84974753170 scopus 로고
    • Convergence of approximation schemes for fully nonlinear second order equations
    • Barles G., and Souganidis P.E. Convergence of approximation schemes for fully nonlinear second order equations. Asymptotic Analysis 4 (1991) 271-283
    • (1991) Asymptotic Analysis , vol.4 , pp. 271-283
    • Barles, G.1    Souganidis, P.E.2
  • 3
    • 0034347336 scopus 로고    scopus 로고
    • On the large time behavior of solutions of Hamilton-Jacobi equations
    • Barles G., and Souganidis P.E. On the large time behavior of solutions of Hamilton-Jacobi equations. SIAM J. Math. Anal. 31 4 (2000) 925-939
    • (2000) SIAM J. Math. Anal. , vol.31 , Issue.4 , pp. 925-939
    • Barles, G.1    Souganidis, P.E.2
  • 4
    • 2342491560 scopus 로고    scopus 로고
    • Large time behaviour of fronts governed by eikonal equations
    • Barles G., and Roquejoffre J.M. Large time behaviour of fronts governed by eikonal equations. Interfaces and Free Boundaries 5 (2003) 83-102
    • (2003) Interfaces and Free Boundaries , vol.5 , pp. 83-102
    • Barles, G.1    Roquejoffre, J.M.2
  • 5
    • 33745549140 scopus 로고    scopus 로고
    • M.C. Concordel, Periodic homogenization of Hamilton-Jacobi equations, PhD thesis, UC Berkeley, 1995
  • 6
    • 0000466871 scopus 로고    scopus 로고
    • Periodic homogenization of Hamilton-Jacobi equation: Additive eigenvalues and variational formula
    • Concordel M.C. Periodic homogenization of Hamilton-Jacobi equation: Additive eigenvalues and variational formula. Indiana Univ. Math. J. 45 (1996) 1095-1117
    • (1996) Indiana Univ. Math. J. , vol.45 , pp. 1095-1117
    • Concordel, M.C.1
  • 8
    • 33745534045 scopus 로고    scopus 로고
    • A. Davini, A. Siconolfi, A Generalized Dynamical Approach to the Large time behavior of solutions of Hamilton-Jacobi equations, SIAM J. Mathematical Analysis, in press
  • 9
    • 0001562857 scopus 로고    scopus 로고
    • Aubry-Mather theory and periodic solutions of the forced Burgers equation
    • E W. Aubry-Mather theory and periodic solutions of the forced Burgers equation. Communication in Pure and Applied Mathematics 52 (1999) 811-828
    • (1999) Communication in Pure and Applied Mathematics , vol.52 , pp. 811-828
  • 10
    • 84974059058 scopus 로고
    • Periodic homogenization of certain nonlinear partial differential equation
    • Evans L.C. Periodic homogenization of certain nonlinear partial differential equation. Proc. Roy. Soc. Edinburgh A 120 (1992) 245-265
    • (1992) Proc. Roy. Soc. Edinburgh A , vol.120 , pp. 245-265
    • Evans, L.C.1
  • 11
    • 2442713751 scopus 로고    scopus 로고
    • A survey of partial differential equations methods in weak KAM theory
    • Evans L.C. A survey of partial differential equations methods in weak KAM theory. Communication in Pure and Applied Mathematics 57 (2004) 445-480
    • (2004) Communication in Pure and Applied Mathematics , vol.57 , pp. 445-480
    • Evans, L.C.1
  • 12
    • 0035589103 scopus 로고    scopus 로고
    • Effective Hamiltonians and averaging for Hamiltonian dynamics I
    • Evans L.C., and Gomes D.A. Effective Hamiltonians and averaging for Hamiltonian dynamics I. Arch. Ration. Mech. Anal. 157 (2001) 1-33
    • (2001) Arch. Ration. Mech. Anal. , vol.157 , pp. 1-33
    • Evans, L.C.1    Gomes, D.A.2
  • 13
    • 0036525374 scopus 로고    scopus 로고
    • Effective Hamiltonians and averaging for Hamiltonian dynamics II
    • Evans L.C., and Gomes D.A. Effective Hamiltonians and averaging for Hamiltonian dynamics II. Arch. Ration. Mech. Anal. 161 (2002) 271-305
    • (2002) Arch. Ration. Mech. Anal. , vol.161 , pp. 271-305
    • Evans, L.C.1    Gomes, D.A.2
  • 14
    • 0037137981 scopus 로고    scopus 로고
    • Semi-Lagrangian schemes for Hamilton-Jacobi equations, discrete representation formulae and Goudonov methods
    • Falcone M., and Ferretti R. Semi-Lagrangian schemes for Hamilton-Jacobi equations, discrete representation formulae and Goudonov methods. J. Comput. Phys. 175 (2002) 559-575
    • (2002) J. Comput. Phys. , vol.175 , pp. 559-575
    • Falcone, M.1    Ferretti, R.2
  • 15
    • 33745570319 scopus 로고    scopus 로고
    • M. Falcone, M. Rorro, A. Siconolfi, Numerical approximation of the effective Hamiltonian and of the Aubry set, in preparation
  • 16
    • 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 327 (1998) 267-270
    • (1998) C. R. Acad. Sci. Paris , vol.327 , pp. 267-270
    • Fathi, A.1
  • 18
    • 11944264666 scopus 로고    scopus 로고
    • PDE aspects of Aubry-Mather theory for quasiconvex Hamiltonians
    • Fathi A., and Siconolfi A. PDE aspects of Aubry-Mather theory for quasiconvex Hamiltonians. Calc. Var. Partial Differential Equations 22 (2005) 185-228
    • (2005) Calc. Var. Partial Differential Equations , vol.22 , pp. 185-228
    • Fathi, A.1    Siconolfi, A.2
  • 19
    • 0346707478 scopus 로고    scopus 로고
    • Convergence of semi-Lagrangian approximations to convex Hamilton-Jacobi equations under (very) large Courant numbers
    • Ferretti R. Convergence of semi-Lagrangian approximations to convex Hamilton-Jacobi equations under (very) large Courant numbers. SIAM J. Numer. Anal. 40 (2002) 2240-2253
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 2240-2253
    • Ferretti, R.1
  • 20
    • 19944362518 scopus 로고    scopus 로고
    • Computing the effective Hamiltonian using a variational approach
    • Gomes D.A., and Oberman A. Computing the effective Hamiltonian using a variational approach. SIAM J. Cont. Opt. 43 (2004) 798-812
    • (2004) SIAM J. Cont. Opt. , vol.43 , pp. 798-812
    • Gomes, D.A.1    Oberman, A.2
  • 22
    • 0141869069 scopus 로고    scopus 로고
    • Computing the effective Hamiltonian in the Majda-Souganidis model of turbulent premixed flames
    • Khouider B., and Bourlioux A. Computing the effective Hamiltonian in the Majda-Souganidis model of turbulent premixed flames. SIAM J. Numer. Anal. 40 (2002) 1330-1353
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 1330-1353
    • Khouider, B.1    Bourlioux, A.2
  • 23
    • 33745580777 scopus 로고    scopus 로고
    • P. Lanucara, M. Rorro, HJPACK: A software package for Hamilton-Jacobi equations, in: SIMAI 2004, VII Congresso Nazionale della Soc. It. di Mat. Appl. e Industriale, Venezia, 2004 (extended abstract)
  • 25
    • 33745542470 scopus 로고    scopus 로고
    • P.L. Lions, G. Papanicolau, S.R.S. Varadhan, Homogenization of Hamilton-Jacobi equations, unpublished preprint, 1987
  • 26
    • 0033475055 scopus 로고    scopus 로고
    • Remarks on the long time behaviour of the solutions of Hamilton-Jacobi equations
    • Namah G., and Roquejoffre J.M. Remarks on the long time behaviour of the solutions of Hamilton-Jacobi equations. Comm. Partial Differential Equations 24 (1999) 883-893
    • (1999) Comm. Partial Differential Equations , vol.24 , pp. 883-893
    • Namah, G.1    Roquejoffre, J.M.2
  • 27
    • 33745565882 scopus 로고    scopus 로고
    • J. Qian, Two approximations for effective Hamiltonians arising from homogenization of Hamilton-Jacobi equations, UCLA, CAM reports, 03-39, 2003
  • 28
    • 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. 80 1 (2001) 85-104
    • (2001) J. Math. Pures Appl. , vol.80 , Issue.1 , pp. 85-104
    • Roquejoffre, J.M.1
  • 29
    • 33745560972 scopus 로고    scopus 로고
    • http://www.caspur.it/hjpack


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.