Gradient semigroups and their dynamical properties
作者： Alexandre N. Carvalho , José A. Langa , James C. Robinson
DOI: 10.1007/978-1-4614-4581-4_5
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摘要: We have already seen that the structure of attractor an autonomous gradient semigroup can be completely described: it is given by union unstable sets equilibria (Theorem 2.43). However, key to definition a (Definition 2.38) existence Lyapunov function, and this very delicate matter.
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sci-hub.se 参考文章(22)
Peter E. Kloeden, Martin Rasmussen, Nonautonomous Dynamical Systems ,(2011)
Charles Conley, Isolated Invariant Sets and the Morse Index American Mathematical Society. ,vol. 38, ,(1978) , 10.1090/CBMS/038
Krzysztof P. Rybakowski, The Homotopy Index and Partial Differential Equations ,(1987)
George R. Sell, Yuncheng You, Dynamics of Evolutionary Equations ,(2002)
Douglas E. Norton, The fundamental theorem of dynamical systems Commentationes Mathematicae Universitatis Carolinae. ,vol. 36, pp. 585- 597 ,(1995)
José A. Langa, G. Łukaszewicz, J. Real, Finite fractal dimension of pullback attractors for non-autonomous 2D Navier–Stokes equations in some unbounded domains Nonlinear Analysis-theory Methods & Applications. ,vol. 66, pp. 735- 749 ,(2007) , 10.1016/J.NA.2005.12.017
Mike Hurley, Chain recurrence, semiflows, and gradients Journal of Dynamics and Differential Equations. ,vol. 7, pp. 437- 456 ,(1995) , 10.1007/BF02219371
Tomás Caraballo, José A. Langa, Zhenxin Liu, Gradient Infinite-Dimensional Random Dynamical Systems Siam Journal on Applied Dynamical Systems. ,vol. 11, pp. 1817- 1847 ,(2012) , 10.1137/120862752
Alexandre N. Carvalho, José A. Langa, An extension of the concept of gradient semigroups which is stable under perturbation Journal of Differential Equations. ,vol. 246, pp. 2646- 2668 ,(2009) , 10.1016/J.JDE.2009.01.007
Konstantin Mischaikow, Hal Smith, Horst R. Thieme, Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions Transactions of the American Mathematical Society. ,vol. 347, pp. 1669- 1685 ,(1995) , 10.1090/S0002-9947-1995-1290727-7