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Volumn 46, Issue 5, 2001, Pages 675-698

Convergence in gradient-like systems which are asymptotically autonomous and analytic

Author keywords

Asymptotically autonomous dynamical process; Gauge; Ginzburg Landau equations; Gradient like system; Lojasiewicz Simon type inequality; Stabilization

Indexed keywords

INTEGRAL EQUATIONS; THEOREM PROVING;

EID: 0013145570     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(00)00145-0     Document Type: Article
Times cited : (67)

References (33)
  • 2
    • 84988159333 scopus 로고
    • On a nonstationary Ginzburg-Landau superconductivity model
    • Z.M. Chen, K.-H. Hoffmann, J. Liang, On a nonstationary Ginzburg-Landau superconductivity model, Math. Methods Appl. Sci. 16 (1993) 855-875.
    • (1993) Math. Methods Appl. Sci. , vol.16 , pp. 855-875
    • Chen, Z.M.1    Hoffmann, K.-H.2    Liang, J.3
  • 5
    • 84947888974 scopus 로고
    • Global existence and uniqueness of solutions of the time-dependent Ginzburg-Landau model for superconductivity
    • Q. Du, Global existence and uniqueness of solutions of the time-dependent Ginzburg-Landau model for superconductivity, Appl. Anal. 53 (1994) 1-18.
    • (1994) Appl. Anal. , vol.53 , pp. 1-18
    • Du, Q.1
  • 7
    • 0040342402 scopus 로고    scopus 로고
    • Convergence for semilinear degenerate parabolic equations in several space dimensions
    • to appear
    • E. Feireisl, F. Simondon, Convergence for semilinear degenerate parabolic equations in several space dimensions, J. Dynamics Differential Equations (1999), to appear.
    • (1999) J. Dynamics Differential Equations
    • Feireisl, E.1    Simondon, F.2
  • 9
    • 0032061639 scopus 로고    scopus 로고
    • Dynamics of the Ginzburg-Landau equations of superconductivity
    • J. Fleckinger-Pellé, H.G. Kaper, P. Takáč, Dynamics of the Ginzburg-Landau equations of superconductivity, Nonlinear Anal. 32 (5) (1998) 647-665.
    • (1998) Nonlinear Anal. , vol.32 , Issue.5 , pp. 647-665
    • Fleckinger-Pellé, J.1    Kaper, H.G.2    Takáč, P.3
  • 10
    • 0000098780 scopus 로고
    • On the theory of superconductivity
    • USSR
    • V.L. Ginzburg, L.D. Landau, On the theory of superconductivity, Zh. Eksp. Teor. Fiz. (USSR) 20, (1950) 1064-1082
    • (1950) Zh. Eksp. Teor. Fiz. , vol.20 , pp. 1064-1082
    • Ginzburg, V.L.1    Landau, L.D.2
  • 11
    • 0010681192 scopus 로고
    • Engl. transl. Pergamon Press, Oxford
    • (Engl. transl. in D. ter Haar, L.D. Landau; Men of Physics, Vol. I, Pergamon Press, Oxford, 1965, pp. 138-167).
    • (1965) Men of Physics , vol.1 , pp. 138-167
    • Ter Haar, D.1    Landau, L.D.2
  • 12
    • 0003293929 scopus 로고
    • Asymptotic Behavior of Dissipative Systems
    • American Mathematical Society, Providence, RI
    • J.K. Hale, Asymptotic Behavior of Dissipative Systems, Math. Surveys and Monographs, Vol. 25, American Mathematical Society, Providence, RI, 1988.
    • (1988) Math. Surveys and Monographs , vol.25
    • Hale, J.K.1
  • 13
    • 0040156406 scopus 로고
    • Asymptotic behavior of gradient-like systems
    • A.R. Bednarek, L. Cesari (Eds.), Academic Press, Inc, New York
    • J.K. Hale, P. Massatt, Asymptotic behavior of gradient-like systems, in: A.R. Bednarek, L. Cesari (Eds.), Dynamical Systems, Vol. II, Academic Press, Inc, New York, 1982, pp. 85-101.
    • (1982) Dynamical Systems , vol.2 , pp. 85-101
    • Hale, J.K.1    Massatt, P.2
  • 14
    • 0002555899 scopus 로고
    • Convergence in gradient-like systems with applications to PDEs
    • J.K. Hale, G. Raugel, Convergence in gradient-like systems with applications to PDEs, Z. Angew. Math. Phys. 43 (1992) 63-124.
    • (1992) Z. Angew. Math. Phys. , vol.43 , pp. 63-124
    • Hale, J.K.1    Raugel, G.2
  • 15
    • 0000746952 scopus 로고    scopus 로고
    • Convergence of solutions of second-order gradient-like systems with analytic nonlinearities
    • A. Haraux, M.A. Jendoubi, Convergence of solutions of second-order gradient-like systems with analytic nonlinearities, J. Differential Equations 144 (1998) 313-320.
    • (1998) J. Differential Equations , vol.144 , pp. 313-320
    • Haraux, A.1    Jendoubi, M.A.2
  • 16
    • 0000617168 scopus 로고
    • Convergence to a positive equilibrium for some nonlinear evolution equations in a ball
    • A. Haraux, P. Poláčik, Convergence to a positive equilibrium for some nonlinear evolution equations in a ball, Acta Math. Univ. Comeniane 2 (1992) 129-141.
    • (1992) Acta Math. Univ. Comeniane , vol.2 , pp. 129-141
    • Haraux, A.1    Poláčik, P.2
  • 17
    • 0003086507 scopus 로고    scopus 로고
    • Convergence of solutions to the equation of quasi-static approximation of viscoelasticity with capillarity
    • K.-H. Hoffmann, P. Rybka, Convergence of solutions to the equation of quasi-static approximation of viscoelasticity with capillarity, J. Math. Anal. Appl. 226 (1998) 61-81.
    • (1998) J. Math. Anal. Appl. , vol.226 , pp. 61-81
    • Hoffmann, K.-H.1    Rybka, P.2
  • 18
    • 11544372290 scopus 로고    scopus 로고
    • A simple unified approach to some convergence theorems of L. Simon
    • M.A. Jendoubi, A simple unified approach to some convergence theorems of L. Simon, J. Funct. Anal. 153 (1998) 197-202.
    • (1998) J. Funct. Anal. , vol.153 , pp. 197-202
    • Jendoubi, M.A.1
  • 19
    • 0000898687 scopus 로고    scopus 로고
    • Convergence of global and bounded solutions of the wave equation with linear dissipation and analytic nonlinearity
    • M.A. Jendoubi, Convergence of global and bounded solutions of the wave equation with linear dissipation and analytic nonlinearity, J. Differential Equations 144 (1998) 302-312.
    • (1998) J. Differential Equations , vol.144 , pp. 302-312
    • Jendoubi, M.A.1
  • 20
    • 0031512221 scopus 로고    scopus 로고
    • Ginzburg-Landau vortices: Dynamics, pinning, and hysteresis
    • F.-H. Lin, Q. Du, Ginzburg-Landau vortices: dynamics, pinning, and hysteresis, SIAM J. Math. Anal. 28 (6) (1997) 1265-1293.
    • (1997) SIAM J. Math. Anal. , vol.28 , Issue.6 , pp. 1265-1293
    • Lin, F.-H.1    Du, Q.2
  • 21
    • 0001132553 scopus 로고
    • Structure of the set of the steady-state solutions and asymptotic behavior of semilinear heat equations
    • P.-L. Lions, Structure of the set of the steady-state solutions and asymptotic behavior of semilinear heat equations, J. Differential Equations 53 (1984) 362-386.
    • (1984) J. Differential Equations , vol.53 , pp. 362-386
    • Lions, P.-L.1
  • 23
    • 0000675919 scopus 로고
    • Convergence of solutions of one-dimensional semilinear heat equations
    • H. Matano, Convergence of solutions of one-dimensional semilinear heat equations, J. Math. Kyoto Univ. 18 (1978) 221-227.
    • (1978) J. Math. Kyoto Univ. , vol.18 , pp. 221-227
    • Matano, H.1
  • 24
    • 0003413877 scopus 로고    scopus 로고
    • Sobolev Gradients and Differential Equations, Springer, Berlin
    • J.W. Neuberger, in: Sobolev Gradients and Differential Equations, Lecture Notes in Mathematics, Vol. 1670, Springer, Berlin, 1997.
    • (1997) Lecture Notes in Mathematics , vol.1670
    • Neuberger, J.W.1
  • 25
    • 16144369367 scopus 로고    scopus 로고
    • Nonconvergent bounded trajectories in semilinear heat equations
    • P. Poláčik, K.P. Rybakowski, Nonconvergent bounded trajectories in semilinear heat equations, J. Differential Equations 124 (1996) 472-494.
    • (1996) J. Differential Equations , vol.124 , pp. 472-494
    • Poláčik, P.1    Rybakowski, K.P.2
  • 26
    • 0001278064 scopus 로고
    • Dynamics of partial differential equations on thin domains
    • G. Raugel, Dynamics of partial differential equations on thin domains, in: Lecture Notes on Dynamical Systems, Vol. 1609, pp. 208-315, 1994.
    • (1994) Lecture Notes on Dynamical Systems , vol.1609 , pp. 208-315
    • Raugel, G.1
  • 27
    • 0033475056 scopus 로고    scopus 로고
    • Convergence of solutions to the Cahn-Hilliard equation
    • P. Rybka, K.-H. Hoffmann, Convergence of solutions to the Cahn-Hilliard equation, Comm. Partial Differential Equations 24 (5& 6) (1999) 1055-1077.
    • (1999) Comm. Partial Differential Equations , vol.24 , Issue.5-6 , pp. 1055-1077
    • Rybka, P.1    Hoffmann, K.-H.2
  • 28
    • 34250510674 scopus 로고
    • A time dependent Ginzburg-Landau equation and its application to the problem of resistivity in the mixed state
    • A. Schmid, A time dependent Ginzburg-Landau equation and its application to the problem of resistivity in the mixed state, Phys. Kondens. Mater. 5 (1966) 302-317.
    • (1966) Phys. Kondens. Mater. , vol.5 , pp. 302-317
    • Schmid, A.1
  • 29
    • 0000137102 scopus 로고
    • Asymptotics for a class of non-linear evolution equations, with applications to geometric problems
    • L. Simon, Asymptotics for a class of non-linear evolution equations, with applications to geometric problems, Ann. Math. 118 (1983) 525-571.
    • (1983) Ann. Math. , vol.118 , pp. 525-571
    • Simon, L.1
  • 30
    • 84963449400 scopus 로고
    • On an evolutionary system of Ginzburg-Landau equations with fixed total magnetic flux
    • Q. Tang, On an evolutionary system of Ginzburg-Landau equations with fixed total magnetic flux, Comm. Partial Differential Equations 20 (1995) 1-36.
    • (1995) Comm. Partial Differential Equations , vol.20 , pp. 1-36
    • Tang, Q.1
  • 31
    • 0000218293 scopus 로고
    • Time dependent Ginzburg-Landau equations of superconductivity
    • Q. Tang, S. Wang, Time dependent Ginzburg-Landau equations of superconductivity, Physica D 88 (1995) 139-166.
    • (1995) Physica D , vol.88 , pp. 139-166
    • Tang, Q.1    Wang, S.2
  • 33
    • 0001883857 scopus 로고
    • Stabilization of solutions of boundary value problems for a second-order parabolic equation with one space variable
    • T.J. Zelenyak, Stabilization of solutions of boundary value problems for a second-order parabolic equation with one space variable, Differentsial'nye Uravneniya 4 (1968) 17-22.
    • (1968) Differentsial'nye Uravneniya , vol.4 , pp. 17-22
    • Zelenyak, T.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.