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Volumn 6, Issue 4, 2007, Pages 1098-1124

A 1d macroscopic phase field model for dislocations and a second order Γ-limit

Author keywords

convergence; Asymptotic development; Dislocations; Phase transitions

Indexed keywords

ABS RESINS; ASYMPTOTIC ANALYSIS; BOUNDARY VALUE PROBLEMS; CRYSTAL DEFECTS; CRYSTALLOGRAPHY; DIFFERENTIAL EQUATIONS; HOOKS; INITIAL VALUE PROBLEMS; PHASE TRANSITIONS;

EID: 55149084384     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/070679181     Document Type: Article
Times cited : (20)

References (23)
  • 1
    • 0032383890 scopus 로고    scopus 로고
    • A nonlocal anisotropic model for phase transition
    • G. ALBERTI and G. BELLETTINI, A nonlocal anisotropic model for phase transition, Math. Ann., 310 (1998), pp. 527-560.
    • (1998) Math. Ann , vol.310 , pp. 527-560
    • ALBERTI, G.1    BELLETTINI, G.2
  • 4
    • 0001482683 scopus 로고
    • Asymptotic development by Γ-convergence
    • G. ANZELLOTTI and S. BALDO, Asymptotic development by Γ-convergence, Appl. Math. Optim., 27 (1993), pp. 105-123.
    • (1993) Appl. Math. Optim , vol.27 , pp. 105-123
    • ANZELLOTTI, G.1    BALDO, S.2
  • 5
    • 0003775635 scopus 로고
    • Progr. Nonlinear Differential Equations Appl. 13, Birkhäuser Verlag, Boston
    • F. BETHUEL, H. BREZIS, and F. HÉLEIN, Ginzburg-Landau Vortices, Progr. Nonlinear Differential Equations Appl. 13, Birkhäuser Verlag, Boston, 1994.
    • (1994) Ginzburg-Landau Vortices
    • BETHUEL, F.1    BREZIS, H.2    HÉLEIN, F.3
  • 6
    • 55149119459 scopus 로고    scopus 로고
    • A symptotic Expansions by Γ-Convergence
    • manuscript
    • A. BRAIDES and L. TRUSKINOWSKY, A symptotic Expansions by Γ-Convergence, manuscript.
    • BRAIDES, A.1    TRUSKINOWSKY, L.2
  • 7
    • 29244478209 scopus 로고    scopus 로고
    • Minimizers for Boundary Reactions: Renormalized Energy, Location of Singularities, and Applications
    • in preparation
    • X. CABRÉ and N. CÓNSUL, Minimizers for Boundary Reactions: Renormalized Energy, Location of Singularities, and Applications, in preparation.
    • CABRÉ, X.1    CÓNSUL, N.2
  • 8
    • 30544441113 scopus 로고    scopus 로고
    • Layer solutions in a half space for boundary reactions
    • X. CABRÉ and J. SOLÀ MORALES, Layer solutions in a half space for boundary reactions, Comm. Pure Appl. Math., 58 (2005), pp. 1678-1732.
    • (2005) Comm. Pure Appl. Math , vol.58 , pp. 1678-1732
    • CABRÉ, X.1    SOLÀ MORALES, J.2
  • 9
    • 33746110773 scopus 로고    scopus 로고
    • Renormalized energy and forces on dislocations
    • P. CERMELLI and G. LEONI, Renormalized energy and forces on dislocations, SIAM J. Math. Anal., 37 (2005), pp. 1131-1160.
    • (2005) SIAM J. Math. Anal , vol.37 , pp. 1131-1160
    • CERMELLI, P.1    LEONI, G.2
  • 10
    • 0003805083 scopus 로고
    • Progr. Nonlinear Differential Equations Appl. 8, Birkhäuser Verlag, Boston
    • G. DAL MASO, An Introduction to Γ-Convergence, Progr. Nonlinear Differential Equations Appl. 8, Birkhäuser Verlag, Boston, 1993.
    • (1993) An Introduction to Γ-Convergence
    • DAL MASO, G.1
  • 12
    • 27844442719 scopus 로고    scopus 로고
    • A. GARRONI and S. MÜLLER, Γ- limit of a phase-field model of dislocations, SIAM J. Math. Anal., 36 (2005), pp. 1943-1964.
    • A. GARRONI and S. MÜLLER, Γ- limit of a phase-field model of dislocations, SIAM J. Math. Anal., 36 (2005), pp. 1943-1964.
  • 13
    • 33745603193 scopus 로고    scopus 로고
    • A variational model for dislocations in the line tension limit
    • A. GARRONI and S. MÜLLER, A variational model for dislocations in the line tension limit, Arch. Ration. Mech. Anal., 181 (2006), pp. 535-578.
    • (2006) Arch. Ration. Mech. Anal , vol.181 , pp. 535-578
    • GARRONI, A.1    MÜLLER, S.2
  • 14
    • 0012940632 scopus 로고
    • Monotonicity of certain functionals under rearrangement
    • A. M. GARSIA and E. RODEMICH, Monotonicity of certain functionals under rearrangement, Ann. Inst. Fourier (Grenoble), 24 (1974), pp. 67-116.
    • (1974) Ann. Inst. Fourier (Grenoble) , vol.24 , pp. 67-116
    • GARSIA, A.M.1    RODEMICH, E.2
  • 15
    • 0010180167 scopus 로고
    • Commutativité de deux foncteurs d'interpolation et applications
    • P. GRISVARD, Commutativité de deux foncteurs d'interpolation et applications, J. Math. Pures Appl. (9), 45 (1966), pp. 143-290.
    • (1966) J. Math. Pures Appl. (9) , vol.45 , pp. 143-290
    • GRISVARD, P.1
  • 17
    • 0036887711 scopus 로고    scopus 로고
    • A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals
    • M. KOSLOWSKI, A. M. CUITIÑO, and M. ORTIZ, A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals, J. Mech. Phys. Solids, 50 (2002), pp. 2597-2635.
    • (2002) J. Mech. Phys. Solids , vol.50 , pp. 2597-2635
    • KOSLOWSKI, M.1    CUITIÑO, A.M.2    ORTIZ, M.3
  • 18
    • 33645787821 scopus 로고    scopus 로고
    • A nonlocal singular perturbation model with periodic well potential
    • M. KURZKE, A nonlocal singular perturbation model with periodic well potential, ESAIM Control Optim. Calc. Var., 12 (2006), pp. 52-63.
    • (2006) ESAIM Control Optim. Calc. Var , vol.12 , pp. 52-63
    • KURZKE, M.1
  • 23
    • 0001469934 scopus 로고
    • Espaces d'interpolation et théorème de Soboleff
    • J. PEETRE, Espaces d'interpolation et théorème de Soboleff, Ann. Inst. Fourier (Grenoble), 16 (1966), pp. 279-317.
    • (1966) Ann. Inst. Fourier (Grenoble) , vol.16 , pp. 279-317
    • PEETRE, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.