메뉴 건너뛰기




Volumn 263-264, Issue , 2004, Pages 171-180

Phase dynamics in the real Ginzburg-Landau equation

Author keywords

Approximation; Pattern formation; Phase diffusion

Indexed keywords


EID: 0942267992     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.200310129     Document Type: Article
Times cited : (25)

References (30)
  • 1
    • 0013332276 scopus 로고
    • Linear and quasilinear parabolic problems
    • Birkhäuser
    • H. Amann, Linear and quasilinear parabolic problems, Monographs in Mathematics (Birkhäuser, 1995).
    • (1995) Monographs in Mathematics
    • Amann, H.1
  • 2
    • 0642313434 scopus 로고
    • Slowly varying fully nonlinear wavetrains in the Ginzburg-Landau equation
    • A. J. Bernoff, Slowly varying fully nonlinear wavetrains in the Ginzburg-Landau equation, Phys. D 30 (3), 363-381 (1988).
    • (1988) Phys. D , vol.30 , Issue.3 , pp. 363-381
    • Bernoff, A.J.1
  • 3
    • 21144479301 scopus 로고
    • Renormalization group and the Ginzburg-Landau equation
    • J. Bricmont and A. Kupiainen, Renormalization group and the Ginzburg-Landau equation, Comm. Math. Phys. 150, 193-208 (1992).
    • (1992) Comm. Math. Phys. , vol.150 , pp. 193-208
    • Bricmont, J.1    Kupiainen, A.2
  • 4
    • 84990739185 scopus 로고
    • Renormalization group and asymptotics of solutions of nonlinear parabolic equations
    • J. Bricmont, A. Kupiainen, and G. Lin, Renormalization group and asymptotics of solutions of nonlinear parabolic equations, Commun. Pure Appl. Math. 47, 893-922 (1994).
    • (1994) Commun. Pure Appl. Math. , vol.47 , pp. 893-922
    • Bricmont, J.1    Kupiainen, A.2    Lin, G.3
  • 5
    • 0000484304 scopus 로고
    • The time dependent amplitude equation for the Swift-Hohenberg problem
    • P. Collet and J.-P. Eckmann, The time dependent amplitude equation for the Swift-Hohenberg problem, Comm. Math. Phys. 132, 139-153 (1990).
    • (1990) Comm. Math. Phys. , vol.132 , pp. 139-153
    • Collet, P.1    Eckmann, J.-P.2
  • 6
    • 0040953231 scopus 로고
    • Diffusive repair for the Ginsburg-Landau equation
    • P. Collet, J.-P. Eckmann, and H. Epstein, Diffusive repair for the Ginsburg-Landau equation, Helv. Phys. Acta 65, 56-92 (1992).
    • (1992) Helv. Phys. Acta , vol.65 , pp. 56-92
    • Collet, P.1    Eckmann, J.-P.2    Epstein, H.3
  • 7
    • 0021390251 scopus 로고
    • Convection patterns in large aspect ratio systems
    • M. C. Cross and A. C. Newell, Convection patterns in large aspect ratio systems, Physica D 10, 299-328 (1984).
    • (1984) Physica D , vol.10 , pp. 299-328
    • Cross, M.C.1    Newell, A.C.2
  • 8
    • 12044252828 scopus 로고
    • Pattern formation outside of equilibrium
    • M. C. Cross and P. C. Hohenberg, Pattern formation outside of equilibrium, Rev. Mod. Phys. 65, 851-1090 (1993).
    • (1993) Rev. Mod. Phys. , vol.65 , pp. 851-1090
    • Cross, M.C.1    Hohenberg, P.C.2
  • 11
    • 22444455115 scopus 로고    scopus 로고
    • Diffusive mixing of stable states in the Ginzburg-Landau equation
    • T. Gallay and A. Mielke, Diffusive mixing of stable states in the Ginzburg-Landau equation, Comm. Math. Phys. 199, 71-97 (1998).
    • (1998) Comm. Math. Phys. , vol.199 , pp. 71-97
    • Gallay, T.1    Mielke, A.2
  • 12
    • 0003304963 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer-Verlag, Berlin-New York
    • D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lectures Notes in Mathematics Vol. 840 (Springer-Verlag, Berlin-New York, 1981).
    • (1981) Lectures Notes in Mathematics , vol.840
    • Henry, D.1
  • 13
    • 84968487166 scopus 로고
    • The porous medium equation in one dimension
    • B. F. Knerr, The porous medium equation in one dimension, Trans. Amer. Math. Soc. 234, 381-415 (1977).
    • (1977) Trans. Amer. Math. Soc. , vol.234 , pp. 381-415
    • Knerr, B.F.1
  • 14
    • 0009395160 scopus 로고    scopus 로고
    • Electrohydrodynamic instabilities in nematic liqud crystals
    • edited by A. Buka and L. Kramer (Springer-Verlag)
    • L. Kramer and W. Pesch, Electrohydrodynamic instabilities in nematic liqud crystals, in Pattern Formation in Liquid Crystals, edited by A. Buka and L. Kramer (Springer-Verlag, 1996), pp. 221-255.
    • (1996) Pattern Formation in Liquid Crystals , pp. 221-255
    • Kramer, L.1    Pesch, W.2
  • 16
    • 0018702717 scopus 로고
    • Stability and fluctuations of a spatially periodic convection flow
    • P. Manneville and Y. Pomeau, Stability and fluctuations of a spatially periodic convection flow, J. Phys. Lett. 40, 609-612 (1979).
    • (1979) J. Phys. Lett. , vol.40 , pp. 609-612
    • Manneville, P.1    Pomeau, Y.2
  • 18
    • 0009940282 scopus 로고    scopus 로고
    • Derivation of the time-dependent Ginzburg-Landau equation on the line
    • I. Melbourne, Derivation of the time-dependent Ginzburg-Landau equation on the line, J. Nonlinear Sci. 8, 1-15 (1998).
    • (1998) J. Nonlinear Sci. , vol.8 , pp. 1-15
    • Melbourne, I.1
  • 19
    • 22644449020 scopus 로고    scopus 로고
    • Steady-state bifurcation with Euclidean symmetry
    • I. Melbourne, Steady-state bifurcation with Euclidean symmetry, Trans. Am. Math. Soc. 351, 1575-1603 (1999).
    • (1999) Trans. Am. Math. Soc. , vol.351 , pp. 1575-1603
    • Melbourne, I.1
  • 20
  • 21
    • 0009956693 scopus 로고
    • Towards a universal theory of patterns
    • T. Passot and A. C. Newell, Towards a universal theory of patterns, Physica D 74, 301-352 (1994).
    • (1994) Physica D , vol.74 , pp. 301-352
    • Passot, T.1    Newell, A.C.2
  • 22
    • 0001656215 scopus 로고
    • Error estimates for the Ginzburg-Landau approximation
    • G. Schneider, Error estimates for the Ginzburg-Landau approximation, J. Appl. Math. Physics (ZAMP) 45, 433-457 (1994).
    • (1994) J. Appl. Math. Physics (ZAMP) , vol.45 , pp. 433-457
    • Schneider, G.1
  • 23
    • 84985386714 scopus 로고
    • Validity and Limitation of the Newell-Whitehead equation
    • G. Schneider, Validity and Limitation of the Newell-Whitehead equation, Mathematische Nachrichten 176, 249-263 (1995).
    • (1995) Mathematische Nachrichten , vol.176 , pp. 249-263
    • Schneider, G.1
  • 24
    • 0032344332 scopus 로고    scopus 로고
    • Nonlinear stability of Taylor-vortices in infinite cylinders
    • G. Schneider, Nonlinear stability of Taylor-vortices in infinite cylinders, Arch. Rational Mech. Analysis 144, 121-200 (1998).
    • (1998) Arch. Rational Mech. Analysis , vol.144 , pp. 121-200
    • Schneider, G.1
  • 25
    • 0033548773 scopus 로고    scopus 로고
    • Global existence results for pattern forming processes in infinite cylindrical domains - Applications to 3D Navier-Stokes problems
    • G. Schneider, Global existence results for pattern forming processes in infinite cylindrical domains - Applications to 3D Navier-Stokes problems, J. Mathématiques Pures Appliquées 78, 265-312 (1999).
    • (1999) J. Mathématiques Pures Appliquées , vol.78 , pp. 265-312
    • Schneider, G.1
  • 26
    • 0001545279 scopus 로고
    • On the validity of Ginzburg-Landau's equation
    • A. van Harten, On the validity of Ginzburg-Landau's equation, J. Nonlinear Science 1, 397-422 (1991).
    • (1991) J. Nonlinear Science , vol.1 , pp. 397-422
    • Van Harten, A.1
  • 28
    • 0942273414 scopus 로고
    • World Sci. Publishing, River Edge, NJ
    • A. van Harten, Modulated modulation equations, in Proceedings of the IUTAM/ISIMM Symposium on Structure and Dynamics of Nonlinear Waves in Fluids, Hannover, 1994, pp. 117-130; Adv. Ser. Nonlinear Dynam. 7 (World Sci. Publishing, River Edge, NJ, 1995).
    • (1995) Adv. Ser. Nonlinear Dynam. , vol.7
  • 29
    • 0000383614 scopus 로고
    • An Introduction to the Mathematical Theory of the Porous Medium Equation
    • Montreal, PQ
    • J. L. Vazquez, An Introduction to the Mathematical Theory of the Porous Medium Equation. Shape Optimization and Free Boundaries (Montreal, PQ, 1990), pp. 347-389; NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 380 (Kluwer Acad. Publ., Dordrecht, 1992).
    • (1990) Shape Optimization and Free Boundaries , pp. 347-389
    • Vazquez, J.L.1
  • 30
    • 0003787266 scopus 로고
    • Kluwer Acad. Publ., Dordrecht
    • J. L. Vazquez, An Introduction to the Mathematical Theory of the Porous Medium Equation. Shape Optimization and Free Boundaries (Montreal, PQ, 1990), pp. 347-389; NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 380 (Kluwer Acad. Publ., Dordrecht, 1992).
    • (1992) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. , vol.380


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.