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Volumn 27, Issue 2, 1996, Pages 424-448

Analyticity of essentially bounded solutions to semilinear parabolic systems and validity of the Ginzburg-Landau equation

Author keywords

Analytic green function; Ginzburg Landau equation; Hardy space; Holomorphic continuation; Weak L solution

Indexed keywords


EID: 0030530210     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141094262518     Document Type: Article
Times cited : (46)

References (37)
  • 2
    • 0000922548 scopus 로고
    • On the possibility of soft and hard turbulence in the complex Ginzburg-Landau equation
    • M. BARTUCCELLI, P. CONSTANTIN, C. R. DOERING, J. D. GIBBON, AND M. GISSELFÄLT, On the possibility of soft and hard turbulence in the complex Ginzburg-Landau equation, Phys. D, 44 (1990), pp. 421-444.
    • (1990) Phys. D , vol.44 , pp. 421-444
    • Bartuccelli, M.1    Constantin, P.2    Doering, C.R.3    Gibbon, J.D.4    Gisselfält, M.5
  • 3
    • 0039991557 scopus 로고
    • Tech. Report 800, Mathematisch Instituut, Rijksuniversiteit Utrecht, Utrecht, The Netherlands
    • P. BOLLERMAN, Validity Results for Ginzburg-Landau's Equation, Tech. Report 800, Mathematisch Instituut, Rijksuniversiteit Utrecht, Utrecht, The Netherlands, 1993.
    • (1993) Validity Results for Ginzburg-Landau's Equation
    • Bollerman, P.1
  • 4
    • 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 (1990), pp. 139-153.
    • (1990) Comm. Math. Phys. , vol.132 , pp. 139-153
    • Collet, P.1    Eckmann, J.-P.2
  • 5
    • 11744315490 scopus 로고
    • Analyticity for the Kuramoto-Sivashinsky equation
    • P. COLLET, J.-P. ECKMANN, H. EPSTEIN, AND J. STUBBE, Analyticity for the Kuramoto-Sivashinsky equation, Phys. D, 67 (1993), pp. 321-326.
    • (1993) Phys. D , vol.67 , pp. 321-326
    • Collet, P.1    Eckmann, J.-P.2    Epstein, H.3    Stubbe, J.4
  • 7
    • 0000287007 scopus 로고
    • Regularity of solutions and the convergence of the Galërkin method in the Ginzburg-Landau equation
    • A. DOELMAN AND E. S. TITI, Regularity of solutions and the convergence of the Galërkin method in the Ginzburg-Landau equation, Numer. Funct. Anal. Optim., 14 (1993), pp. 299-321.
    • (1993) Numer. Funct. Anal. Optim. , vol.14 , pp. 299-321
    • Doelman, A.1    Titi, E.S.2
  • 8
    • 38149143087 scopus 로고
    • On the Cauchy problem for a generalized Ginzburg-Landau equation
    • J. DUAN AND P. HOLMES, On the Cauchy problem for a generalized Ginzburg-Landau equation, Nonlinear Anal., 22 (1994), pp. 1033-1040.
    • (1994) Nonlinear Anal. , vol.22 , pp. 1033-1040
    • Duan, J.1    Holmes, P.2
  • 9
    • 0000815546 scopus 로고
    • Regularity, approximation and asymptotic dynamics for a generalized Ginzburg-Landau equation
    • J. DUAN, P. HOLMES, AND E. S. TITI, Regularity, approximation and asymptotic dynamics for a generalized Ginzburg-Landau equation, Nonlinearity, 6 (1993), pp. 915-933.
    • (1993) Nonlinearity , vol.6 , pp. 915-933
    • Duan, J.1    Holmes, P.2    Titi, E.S.3
  • 10
    • 51249162531 scopus 로고
    • The Ginzburg-Landau manifold is an attractor
    • V. ECKHAUS, The Ginzburg-Landau manifold is an attractor, J. Nonlinear Sci., 3 (1993), pp. 329-348.
    • (1993) J. Nonlinear Sci. , vol.3 , pp. 329-348
    • Eckhaus, V.1
  • 12
    • 33746636159 scopus 로고
    • Gevrey class regularity for the solutions of the Navier-Stokes equations
    • C. FOIAS AND R. TEMAM, Gevrey class regularity for the solutions of the Navier-Stokes equations, J. Funct. Anal., 84 (1989), pp. 359-369.
    • (1989) J. Funct. Anal. , vol.84 , pp. 359-369
    • Foias, C.1    Temam, R.2
  • 13
    • 0000270362 scopus 로고
    • On the regularity of the solutions of nonlinear elliptic and parabolic systems of partial differential equations
    • A. FRIEDMAN, On the regularity of the solutions of nonlinear elliptic and parabolic systems of partial differential equations, J. Math. Mech., 7 (1958), pp. 43-59.
    • (1958) J. Math. Mech. , vol.7 , pp. 43-59
    • Friedman, A.1
  • 14
    • 0003737629 scopus 로고
    • Holt, Rinehart, and Winston, New York, London
    • _, Partial Differential Equations, Holt, Rinehart, and Winston, New York, London, 1969.
    • (1969) Partial Differential Equations
  • 15
    • 0001545279 scopus 로고
    • On the validity of the Ginzburg-Landau equation
    • A. VAN HARTEN, On the validity of the Ginzburg-Landau equation, J. Nonlinear Sci., 1 (1991), pp. 397-422.
    • (1991) J. Nonlinear Sci. , vol.1 , pp. 397-422
    • Van Harten, A.1
  • 16
    • 0025523018 scopus 로고
    • Smallest scale estimates for the Navier-Stokes equations for incompressible fluids
    • W. D. HENSHAW, H.-O. KREISS, AND L. G. REYNA, Smallest scale estimates for the Navier-Stokes equations for incompressible fluids, Arch. Rational Mech. Anal., 112 (1990), pp. 21-44.
    • (1990) Arch. Rational Mech. Anal. , vol.112 , pp. 21-44
    • Henshaw, W.D.1    Kreiss, H.-O.2    Reyna, L.G.3
  • 20
    • 0000650508 scopus 로고
    • Long wavelength instabilities of square patterns
    • R. B. HOYLE, Long wavelength instabilities of square patterns, Phys. D, 67 (1993), pp. 198-223.
    • (1993) Phys. D , vol.67 , pp. 198-223
    • Hoyle, R.B.1
  • 22
    • 84971162773 scopus 로고
    • The validity of modulation equations for extended systems with cubic nonlinearities
    • P. KIRRMANN, G. SCHNEIDER, AND A. MIELKE, The validity of modulation equations for extended systems with cubic nonlinearities, Proc. Roy. Soc. Edinburgh Sect. A, 122 (1992), pp. 85-91.
    • (1992) Proc. Roy. Soc. Edinburgh Sect. A , vol.122 , pp. 85-91
    • Kirrmann, P.1    Schneider, G.2    Mielke, A.3
  • 23
    • 0040584668 scopus 로고
    • Espaces de fonctions et distributions du type de Gevrey et problemes aux limites paraboliques
    • J. L. LIONS AND E. MAGENES, Espaces de fonctions et distributions du type de Gevrey et problemes aux limites paraboliques, Ann. Mat. Pura Appl., 68 (1965), pp. 341-418.
    • (1965) Ann. Mat. Pura Appl. , vol.68 , pp. 341-418
    • Lions, J.L.1    Magenes, E.2
  • 24
    • 0040584639 scopus 로고
    • Espaces du type de Gevrey et problemes aux limites pour diverses classes d'equations d'evolution
    • _, Espaces du type de Gevrey et problemes aux limites pour diverses classes d'equations d'evolution, Ann. Mat. Pura Appl., 72 (1966), pp. 343-394.
    • (1966) Ann. Mat. Pura Appl. , vol.72 , pp. 343-394
  • 25
    • 0000113520 scopus 로고
    • Gevrey class regularity and approximate inertial manifolds for the Kuramoto-Sivashinsky equation
    • X. LIU, Gevrey class regularity and approximate inertial manifolds for the Kuramoto-Sivashinsky equation, Phys. D, 50 (1991), pp. 135-151.
    • (1991) Phys. D , vol.50 , pp. 135-151
    • Liu, X.1
  • 26
    • 34249931751 scopus 로고
    • On the regularity of solutions of the nonstationary Navier-Stokes equations
    • Springer-Verlag, New York, Heidelberg, Berlin
    • K. MASUDA, On the regularity of solutions of the nonstationary Navier-Stokes equations, Lecture Notes in Math., 771, Springer-Verlag, New York, Heidelberg, Berlin, 1980, pp. 360-370.
    • (1980) Lecture Notes in Math , vol.771 , pp. 360-370
    • Masuda, K.1
  • 27
    • 0039399433 scopus 로고
    • Regularity of solutions of partial differential equations, I
    • _, Regularity of solutions of partial differential equations, I, Comment. Math. Univ. St. Paul, 42 (1993), pp. 93-100.
    • (1993) Comment. Math. Univ. St. Paul , vol.42 , pp. 93-100
  • 29
    • 0014662728 scopus 로고
    • Finite bandwidth, finite amplitude convection
    • A. C. NEWELL AND J. A. WHITEHEAD, Finite bandwidth, finite amplitude convection, J. Fluid Mech., 38 (1969), pp. 279-303.
    • (1969) J. Fluid Mech. , vol.38 , pp. 279-303
    • Newell, A.C.1    Whitehead, J.A.2
  • 30
    • 0019666457 scopus 로고
    • Planform selection by finite-amplitude thermal convection between poorly conducting slabs
    • M. R. E. PROCTOR, Planform selection by finite-amplitude thermal convection between poorly conducting slabs, J. Fluid Mech., 113 (1981), pp. 469-485.
    • (1981) J. Fluid Mech. , vol.113 , pp. 469-485
    • Proctor, M.R.E.1
  • 31
    • 0039399453 scopus 로고
    • Ph.D. Thesis, Institut für Mathematik, Universität Stuttgart, Stuttgart, Germany, in German
    • G. SCHNEIDER, Die Gültigkeit der Ginzburg-Landau-approximation, Ph.D. Thesis, Institut für Mathematik, Universität Stuttgart, Stuttgart, Germany, 1992 (in German).
    • (1992) Die Gültigkeit der Ginzburg-Landau-approximation
    • Schneider, G.1
  • 32
    • 0001656215 scopus 로고
    • Error estimates for the Ginzburg-Landau approximation
    • _, Error estimates for the Ginzburg-Landau approximation, Z. Angew. Math. Phys., 45 (1994), pp. 1-24.
    • (1994) Z. Angew. Math. Phys. , vol.45 , pp. 1-24
  • 35
    • 0007642894 scopus 로고
    • Invariant 2-tori in the time-dependent Ginzburg-Landau equation
    • P. TAKÁČ, Invariant 2-tori in the time-dependent Ginzburg-Landau equation, Nonlinearity, 5 (1992), pp. 289-321.
    • (1992) Nonlinearity , vol.5 , pp. 289-321
    • Takáč, P.1
  • 36
    • 84972553910 scopus 로고
    • On differentiability and analyticity of solutions of weighted elliptic boundary value problems
    • H. TANABE, On differentiability and analyticity of solutions of weighted elliptic boundary value problems, Osaka J. Math., 2 (1965), pp. 163-190.
    • (1965) Osaka J. Math. , vol.2 , pp. 163-190
    • Tanabe, H.1


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