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Volumn 23, Issue 3, 2009, Pages 785-826

Homogenization of some particle systems with two-body interactions and of the dislocation dynamics

Author keywords

Dislocation dynamics; Hamilton Jacobi equations; Integro differential operators; L vy operator; Moving fronts; Particle systems; Periodic homogenization; Slep ev formulation; Two body interactions

Indexed keywords


EID: 63049095153     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2009.23.785     Document Type: Article
Times cited : (57)

References (25)
  • 2
    • 0030351484 scopus 로고    scopus 로고
    • Viscosity solutions of nonlinear integro-differential equations
    • O. Alvarez and A. Tourin, Viscosity solutions of nonlinear integro-differential equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, 13 (1996), 293-317.
    • (1996) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.13 , pp. 293-317
    • Alvarez, O.1    Tourin, A.2
  • 4
    • 48749143267 scopus 로고
    • The discrete frenkel-Kontorova model and its extensions
    • S. Aubry and P. Y. Le Daeron, The discrete frenkel-Kontorova model and its extensions, Physica D, 8 (1983), 381-422.
    • (1983) Physica D , vol.8 , pp. 381-422
    • Aubry, S.1    Le Daeron, P.Y.2
  • 6
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M.G. Crandall, H. Ishii and P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.), 27 (1992), 1-67.
    • (1992) Bull. Amer. Math. Soc. (N.S.) , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 7
    • 56649091070 scopus 로고    scopus 로고
    • Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics
    • F. Da Lio, N. Forcadel and R. Monneau, Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics, Journal of the European Mathematical Society, 10 (2008), 1105-1119.
    • (2008) Journal of the European Mathematical Society , vol.10 , pp. 1105-1119
    • Da Lio, F.1    Forcadel, N.2    Monneau, R.3
  • 9
    • 3242755908 scopus 로고    scopus 로고
    • Dynamics scaling in a simple one-dimensional model of dislocation activity
    • J. Deslippe, R. Tesdtrom, M. S. Daw, D. Chrzan, T. Neeraj and M. Mills, Dynamics scaling in a simple one-dimensional model of dislocation activity, Phil. Mag., 84 (2004), 2445-2454.
    • (2004) Phil. Mag , vol.84 , pp. 2445-2454
    • Deslippe, J.1    Tesdtrom, R.2    Daw, M.S.3    Chrzan, D.4    Neeraj, T.5    Mills, M.6
  • 10
    • 84971110219 scopus 로고
    • The perturbed test function method for viscosity solutions of nonlinear PDE
    • L. C. Evans, The perturbed test function method for viscosity solutions of nonlinear PDE, Proc. Roy. Soc. Edinburgh Sect. A, 111 (1989), 359-375.
    • (1989) Proc. Roy. Soc. Edinburgh Sect. A , vol.111 , pp. 359-375
    • Evans, L.C.1
  • 11
    • 84974059058 scopus 로고
    • Periodic homogenisation of certain fully nonlinear partial differential equations
    • L. C. Evans, Periodic homogenisation of certain fully nonlinear partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A, 120 (1992), 245-265.
    • (1992) Proc. Roy. Soc. Edinburgh Sect. A , vol.120 , pp. 245-265
    • Evans, L.C.1
  • 12
    • 63049109432 scopus 로고    scopus 로고
    • Thèse de Doctorat, Ecole Nationnale des Ponts et Chaussées
    • A. Ghorbel, "Thèse de Doctorat," Ecole Nationnale des Ponts et Chaussées, 2007.
    • (2007)
    • Ghorbel, A.1
  • 13
    • 63049130081 scopus 로고    scopus 로고
    • A numerical study for the homogenization of one-dimensional models describing the motion of dislocations
    • Preprint
    • A. Ghorbel, P. Hoch and R. Monneau, A numerical study for the homogenization of one-dimensional models describing the motion of dislocations, Preprint.
    • Ghorbel, A.1    Hoch, P.2    Monneau, R.3
  • 14
    • 0015362460 scopus 로고    scopus 로고
    • A. K. Head, 1972a, Phil. Mag., 26, 43; 1972b, 26, 55; 1972c, 26, 65.
    • A. K. Head, 1972a, Phil. Mag., 26, 43; 1972b, 26, 55; 1972c, 26, 65.
  • 16
    • 23144444560 scopus 로고    scopus 로고
    • Rotation number of the overdamped Frenkel-Kontorova model with ac-driving
    • B. Hu, W.-X. Qin and Z. Zheng, Rotation number of the overdamped Frenkel-Kontorova model with ac-driving, Physica D, 208 (2005), 172-190.
    • (2005) Physica D , vol.208 , pp. 172-190
    • Hu, B.1    Qin, W.-X.2    Zheng, Z.3
  • 17
    • 14244266989 scopus 로고    scopus 로고
    • A non-local regularization of first order Hamilton-Jacobi equations
    • C. Imbert, A non-local regularization of first order Hamilton-Jacobi equations, Journal of Differential Equations, 211 (2005), 218-246.
    • (2005) Journal of Differential Equations , vol.211 , pp. 218-246
    • Imbert, C.1
  • 19
    • 40249111521 scopus 로고    scopus 로고
    • Homogeneisation of first order equations with (u/ε)-periodic Hamiltonians. Part II: Application to dislocation dynamics
    • C. Imbert, R. Monneau and E. Rouy, Homogeneisation of first order equations with (u/ε)-periodic Hamiltonians. Part II: application to dislocation dynamics, Comm. Partial Differential Equations, 33 (2008), 479-516.
    • (2008) Comm. Partial Differential Equations , vol.33 , pp. 479-516
    • Imbert, C.1    Monneau, R.2    Rouy, E.3
  • 20
    • 84972546686 scopus 로고
    • Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor
    • H. Ishii and P. E. Souganidis, Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor, Tohoku Math. J. (2), 47 (1995), 227-250.
    • (1995) Tohoku Math. J. (2) , vol.47 , pp. 227-250
    • Ishii, H.1    Souganidis, P.E.2
  • 23
    • 0036012980 scopus 로고    scopus 로고
    • Gradient systems with wiggly energies and related averaging problems
    • G. Menon, Gradient systems with wiggly energies and related averaging problems, Arch. Ration. Mech. Anal., 162 (2002), 193-246.
    • (2002) Arch. Ration. Mech. Anal , vol.162 , pp. 193-246
    • Menon, G.1
  • 25
    • 0037209552 scopus 로고    scopus 로고
    • Approximation schemes for propagation of fronts with nonlocal velocities and Neumann boundary conditions
    • D. Slepčev, Approximation schemes for propagation of fronts with nonlocal velocities and Neumann boundary conditions, Nonlinear Anal., 52 (2003), 79-115.
    • (2003) Nonlinear Anal , vol.52 , pp. 79-115
    • Slepčev, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.