메뉴 건너뛰기




Volumn 190, Issue 1, 2008, Pages 141-187

The Toda system and clustering interfaces in the Allen-Cahn equation

Author keywords

[No Author keywords available]

Indexed keywords


EID: 50249108359     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-008-0143-3     Document Type: Article
Times cited : (65)

References (40)
  • 1
    • 0346856926 scopus 로고    scopus 로고
    • Motion of a droplet by surface tension along the boundary
    • 3
    • N. Alikakos X. Chen G. Fusco 2000 Motion of a droplet by surface tension along the boundary Cal. Var. PDE 11 3 233 306
    • (2000) Cal. Var. PDE , vol.11 , pp. 233-306
    • Alikakos, N.1    Chen, X.2    Fusco, G.3
  • 2
    • 0018480694 scopus 로고
    • A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening
    • S. Allen J.W. Cahn 1979 A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening Acta. Metall. 27 1084 1095
    • (1979) Acta. Metall. , vol.27 , pp. 1084-1095
    • Allen, S.1    Cahn, J.W.2
  • 3
    • 44949278065 scopus 로고
    • Motion by the mean curvature as the singular limit of Ginzburg-Landau dynamics
    • L. Bronsard R.V. Kohn 1992 Motion by the mean curvature as the singular limit of Ginzburg-Landau dynamics J. Differ. Equ. 90 211 237
    • (1992) J. Differ. Equ. , vol.90 , pp. 211-237
    • Bronsard, L.1    Kohn, R.V.2
  • 4
    • 0030306038 scopus 로고    scopus 로고
    • On the existence of high multiplicity interfaces
    • L. Bronsard B. Stoth 1996 On the existence of high multiplicity interfaces Math. Res. Lett. 3 117 151
    • (1996) Math. Res. Lett. , vol.3 , pp. 117-151
    • Bronsard, L.1    Stoth, B.2
  • 5
    • 84954653751 scopus 로고
    • Exponential decay to stable states in phase transitions via a double log-transformation
    • 12
    • M. Bardi B. Perthame 1990 Exponential decay to stable states in phase transitions via a double log-transformation Comm. Partial Differ. Equ. 15 12 1649 1669
    • (1990) Comm. Partial Differ. Equ. , vol.15 , pp. 1649-1669
    • Bardi, M.1    Perthame, B.2
  • 6
    • 84990648271 scopus 로고
    • Uniform convergence of a singular perturbation problem
    • 1
    • L. Caffarelli A. Cordoba 1995 Uniform convergence of a singular perturbation problem Comm. Pure Appl. Math. 48 1 1 12
    • (1995) Comm. Pure Appl. Math. , vol.48 , pp. 1-12
    • Caffarelli, L.1    Cordoba, A.2
  • 7
    • 0001731871 scopus 로고
    • Instability results for reaction diffusion equations with Neumann boundary conditions
    • 2
    • R. Casten C.J. Holland 1978 Instability results for reaction diffusion equations with Neumann boundary conditions J. Differ. Equ. 27 2 266 273
    • (1978) J. Differ. Equ. , vol.27 , pp. 266-273
    • Casten, R.1    Holland, C.J.2
  • 8
    • 0001249829 scopus 로고
    • Generation and propagation of interfaces in reaction-diffusion equations
    • X. Chen 1992 Generation and propagation of interfaces in reaction-diffusion equations J. Differ. Equ. 96 116 141
    • (1992) J. Differ. Equ. , vol.96 , pp. 116-141
    • Chen, X.1
  • 9
    • 0000161576 scopus 로고
    • Geometrical evolution of developed interfaces
    • 5
    • P. de Mottoni M. Schatzman 1995 Geometrical evolution of developed interfaces Trans. Am. Math. Soc. 347 5 1533 1589
    • (1995) Trans. Am. Math. Soc. , vol.347 , pp. 1533-1589
    • De Mottoni, P.1    Schatzman, M.2
  • 10
    • 0041972657 scopus 로고    scopus 로고
    • An elementary construction of complex patterns in nonlinear Schrodinger equations
    • 5
    • M. del Pino P. Felmer Tanaka K. Kazunaga 2002 An elementary construction of complex patterns in nonlinear Schrodinger equations Nonlinearity 15 5 1653 1671
    • (2002) Nonlinearity , vol.15 , pp. 1653-1671
    • Del Pino, M.1    Felmer, P.2    Tanaka3    Kazunaga, K.4
  • 11
    • 0042854704 scopus 로고    scopus 로고
    • Radial solutions in the slightly supercritical Brezis-Nirenberg problem
    • 2
    • M. del Pino J. Dolbeault M. Musso 2003 radial solutions in the slightly supercritical Brezis-Nirenberg problem J. Differ. Equ. 193 2 280 306
    • (2003) J. Differ. Equ. , vol.193 , pp. 280-306
    • Del Pino, M.1    Dolbeault, J.2    Musso, M.3
  • 12
    • 33751518021 scopus 로고    scopus 로고
    • Concentration on curves for nonlinear Schrödinger equations
    • 1
    • M. del Pino M. Kowalczyk J. Wei 2007 Concentration on curves for nonlinear Schrödinger equations Comm. Pure Appl. Math. 60 1 113 146
    • (2007) Comm. Pure Appl. Math. , vol.60 , pp. 113-146
    • Del Pino, M.1    Kowalczyk, M.2    Wei, J.3
  • 13
    • 23044530537 scopus 로고    scopus 로고
    • The Gierer & Meinhardt system: The breaking of homoclinics and multi-bump ground states
    • 3
    • M. del Pino M. Kowalczyk X. Chen 2001 The Gierer & Meinhardt system: the breaking of homoclinics and multi-bump ground states Commun. Contemp. Math. 3 3 419 439
    • (2001) Commun. Contemp. Math. , vol.3 , pp. 419-439
    • Del Pino, M.1    Kowalczyk, M.2    Chen, X.3
  • 14
    • 0038936057 scopus 로고    scopus 로고
    • Slow dynamics of interfaces in the Allen-Cahn equation on a strip-like domain
    • 3
    • S.-I. Ei E. Yanagida 1998 Slow dynamics of interfaces in the Allen-Cahn equation on a strip-like domain SIAM J. Math. Anal. 29 3 555 595
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 555-595
    • Ei, S.-I.1    Yanagida, E.2
  • 15
  • 16
    • 3042602719 scopus 로고    scopus 로고
    • Closed geodesics on oval surfaces and pattern formation
    • 2
    • C.E. Garza-Hume P. Padilla 2003 Closed geodesics on oval surfaces and pattern formation Comm. Anal. Geom. 11 2 223 233
    • (2003) Comm. Anal. Geom. , vol.11 , pp. 223-233
    • Garza-Hume, C.E.1    Padilla, P.2
  • 17
    • 0010598327 scopus 로고    scopus 로고
    • Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory
    • 1
    • J.E. Hutchinson Y. Tonegawa 2000 Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory Calc. Var. Partial Differ. Equ. 10 1 49 84
    • (2000) Calc. Var. Partial Differ. Equ. , vol.10 , pp. 49-84
    • Hutchinson, J.E.1    Tonegawa, Y.2
  • 18
    • 84972493979 scopus 로고
    • Convergence of the Allen-Cahn equation to the Brakke's motion by mean curvature
    • T. Ilmanen 1993 Convergence of the Allen-Cahn equation to the Brakke's motion by mean curvature J. Differ. Geom. 38 417 461
    • (1993) J. Differ. Geom. , vol.38 , pp. 417-461
    • Ilmanen, T.1
  • 20
    • 0000825718 scopus 로고    scopus 로고
    • On interacting bumps of semi-classical states of nonlinear Schrodinger equations
    • 7-9
    • X. Kang J. Wei 2000 On interacting bumps of semi-classical states of nonlinear Schrodinger equations Adv. Differ. Equ. 5 7-9 899 928
    • (2000) Adv. Differ. Equ. , vol.5 , pp. 899-928
    • Kang, X.1    Wei, J.2
  • 21
    • 0002366904 scopus 로고
    • Generalized motion by mean curvature with Neumann conditions and the Allen-Cahn model for phase transitions
    • 2
    • M. Katsoulakis G.T. Kossioris F. Reitich 1995 Generalized motion by mean curvature with Neumann conditions and the Allen-Cahn model for phase transitions J. Geom. Anal. 5 2 255 279
    • (1995) J. Geom. Anal. , vol.5 , pp. 255-279
    • Katsoulakis, M.1    Kossioris, G.T.2    Reitich, F.3
  • 22
    • 84975988204 scopus 로고
    • Local minimizers and singular perturbations
    • R.V. Kohn P. Sternberg 1989 Local minimizers and singular perturbations Proc. R. Soc. Edinburgh 111 A 69 84
    • (1989) Proc. R. Soc. Edinburgh , vol.111 , pp. 69-84
    • Kohn, R.V.1    Sternberg, P.2
  • 23
    • 0000876641 scopus 로고
    • The solution to a generalized Toda lattice and representation theory
    • B Konstant 1979 The solution to a generalized Toda lattice and representation theory Adv. Math. 34 195 338
    • (1979) Adv. Math. , vol.34 , pp. 195-338
    • Konstant, B.1
  • 24
    • 24944545330 scopus 로고    scopus 로고
    • On the existence and Morse index of solutions to the Allen-Cahn equation in two dimensions
    • 1
    • M. Kowalczyk 2005 On the existence and Morse index of solutions to the Allen-Cahn equation in two dimensions Ann. Mat. Pura Appl. 184 1 17 52
    • (2005) Ann. Mat. Pura Appl. , vol.184 , pp. 17-52
    • Kowalczyk, M.1
  • 25
    • 0036425683 scopus 로고    scopus 로고
    • Boundary concentration phenomena for a singularly perturbed elliptic problem
    • 12
    • A. Malchiodi M. Montenegro 2002 Boundary concentration phenomena for a singularly perturbed elliptic problem Comm. Pure Appl. Math. 55 12 1507 1568
    • (2002) Comm. Pure Appl. Math. , vol.55 , pp. 1507-1568
    • Malchiodi, A.1    Montenegro, M.2
  • 26
    • 4043167077 scopus 로고    scopus 로고
    • Multidimensional boundary layers for a singularly perturbed Neumann problem
    • 1
    • A. Malchiodi M. Montenegro 2004 Multidimensional boundary layers for a singularly perturbed Neumann problem Duke Math. J. 124 1 105 143
    • (2004) Duke Math. J. , vol.124 , pp. 105-143
    • Malchiodi, A.1    Montenegro, M.2
  • 27
    • 13844306817 scopus 로고    scopus 로고
    • Multiple clustered layer solutions for semilinear Neumann problems on a ball
    • 2
    • A. Malchiodi W.-M. Ni J. Wei 2005 Multiple clustered layer solutions for semilinear Neumann problems on a ball Ann. Inst. H. Poincare Anal. Non Lineaire 22 2 143 163
    • (2005) Ann. Inst. H. Poincare Anal. Non Lineaire , vol.22 , pp. 143-163
    • Malchiodi, A.1    Ni, W.-M.2    Wei, J.3
  • 29
    • 34250109116 scopus 로고
    • The gradient theory of phase transitions and the minimal interface criterion
    • 2
    • L. Modica 1987 The gradient theory of phase transitions and the minimal interface criterion Arch. Rational Mech. Anal. 98 2 123 142
    • (1987) Arch. Rational Mech. Anal. , vol.98 , pp. 123-142
    • Modica, L.1
  • 30
    • 85009592686 scopus 로고
    • Asymptotic behavior and stability of solutions of semilinear diffusion equations
    • 2
    • H. Matano 1979 Asymptotic behavior and stability of solutions of semilinear diffusion equations Publ. Res. Inst. Math. Sci. 15 2 401 454
    • (1979) Publ. Res. Inst. Math. Sci. , vol.15 , pp. 401-454
    • Matano, H.1
  • 31
    • 0000641586 scopus 로고
    • Finitely many mass points on the line under the influence of an exponential potential-an integrable system
    • Dynamical systems, theory and applications (Rencontres, BattelleRes. Inst., Seattle, Wash.) Springer, Berlin
    • Moser, J.: Finitely many mass points on the line under the influence of an exponential potential-an integrable system. Dynamical systems, theory and applications (Rencontres, BattelleRes. Inst., Seattle, Wash., 1974), pp. 467-497. Lecture Notes in Phys., Vol. 38, Springer, Berlin, 1975
    • (1974) Lecture Notes in Phys. , vol.38 , pp. 467-497
    • Moser, J.1
  • 32
    • 0038626226 scopus 로고    scopus 로고
    • Multi-layered stationary solutions for a spatially inhomogeneous Allen-Cahn equation
    • 1
    • K. Nakashima 2003 Multi-layered stationary solutions for a spatially inhomogeneous Allen-Cahn equation J. Differ. Equ. 191 1 234 276
    • (2003) J. Differ. Equ. , vol.191 , pp. 234-276
    • Nakashima, K.1
  • 33
    • 0141479615 scopus 로고    scopus 로고
    • Clustering layers and boundary layers in spatially inhomogeneous phase transition problems
    • 1
    • K. Nakashima K. Tanaka 2003 Clustering layers and boundary layers in spatially inhomogeneous phase transition problems Ann. Inst. H. Poincare Anal. Non Lineaire 20 1 107 143
    • (2003) Ann. Inst. H. Poincare Anal. Non Lineaire , vol.20 , pp. 107-143
    • Nakashima, K.1    Tanaka, K.2
  • 34
    • 2642588420 scopus 로고    scopus 로고
    • From the constant mean curvature hypersurfaces to the gradient theory of phase transitions
    • 3
    • F. Pacard M. Ritoré 2003 From the constant mean curvature hypersurfaces to the gradient theory of phase transitions J. Differ. Geom. 64 3 359 423
    • (2003) J. Differ. Geom. , vol.64 , pp. 359-423
    • Pacard, F.1    Ritoré, M.2
  • 35
    • 0040633198 scopus 로고    scopus 로고
    • On the convergence of stable phase transitions
    • 6
    • P. Padilla Y. Tonegawa 1998 On the convergence of stable phase transitions Comm. Pure Appl. Math. 51 6 551 579
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 551-579
    • Padilla, P.1    Tonegawa, Y.2
  • 37
    • 0037695861 scopus 로고    scopus 로고
    • Ginzburg-Landau equation and motion by mean curvature, Part I: Convergence, Part II: Development of the initial interface
    • Part II 477-491
    • Soner, H.M.: Ginzburg-Landau equation and motion by mean curvature, Part I: Convergence, Part II: Development of the initial interface. J. Geom. Anal. 7(3), (1997), Part I 437-455, Part II 477-491
    • (1997) J. Geom. Anal. , vol.7 , Issue.3 PART I , pp. 437-455
    • Soner, H.M.1
  • 38
    • 34250095380 scopus 로고
    • The effect of a singular perturbation on nonconvex variational problems
    • 3
    • P. Sternberg 1988 The effect of a singular perturbation on nonconvex variational problems Arch. Rational Mech. Anal. 101 3 209 260
    • (1988) Arch. Rational Mech. Anal. , vol.101 , pp. 209-260
    • Sternberg, P.1
  • 39
    • 0032370858 scopus 로고    scopus 로고
    • Connectivity of phase boundaries in strictly convex domains
    • 4
    • P. Sternberg K. Zumbrun 1998 Connectivity of phase boundaries in strictly convex domains Arch. Rational Mech. Anal. 141 4 375 400
    • (1998) Arch. Rational Mech. Anal. , vol.141 , pp. 375-400
    • Sternberg, P.1    Zumbrun, K.2
  • 40
    • 0037119540 scopus 로고    scopus 로고
    • Phase field model with a variable chemical potential
    • 4
    • Y. Tonegawa 2002 Phase field model with a variable chemical potential Proc. R. Soc. Edinburgh Sect. A 132 4 993 1019
    • (2002) Proc. R. Soc. Edinburgh Sect. a , vol.132 , pp. 993-1019
    • Tonegawa, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.