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A minimal approach to the theory of global attractors
1. | Institute for Information Transmission Problems, Russian Academy of Sciences, Bolshoy Karetniy 19, Moscow 101447, Russian Federation |
2. | Dipartimento di Matematica “Francesco Brioschi”, Politecnico di Milano, Via Bonardi 9, Milano 20133, Italy, Italy |
References:
[1] |
A. V. Babin and M. I. Vishik, "Attractors of Evolution Equations," Studies in Mathematics and its Applications, 25, North-Holland Publishing Co., Amsterdam, 1992. |
[2] |
V. V. Chepyzhov and M. I. Vishik, "Attractors for Equations of Mathematical Physics,'' American Mathematical Society Colloquium Publications, 49, American Mathematical Society, Providence, RI, 2002. |
[3] |
J. K. Hale, "Asymptotic Behavior of Dissipative Systems," Mathematical Surveys and Monographs, 25, American Mathematical Society, Providence, RI, 1988. |
[4] |
A. Haraux, "Systèmes Dynamiques Dissipatifs et Applications," Recherches en Mathématiques Appliquées, 17, Masson, Paris, 1991. |
[5] |
A. Miranville and S. Zelik, Attractors for dissipative partial differential equations in bounded and unbounded domains, in "Handbook of Differential Equations: Evolutionary Equations," Vol. IV, Elsevier/North-Holland, Amsterdam, (2008), 103-200. |
[6] |
V. Pata and S. Zelik, A result on the existence of global attractors for semigroups of closed operators, Commun. Pure Appl. Anal., 6 (2007), 481-486.
doi: 10.3934/cpaa.2007.6.481. |
[7] |
V. Pata and S. Zelik, Attractors and their regularity for 2-D wave equation with nonlinear damping, Adv. Math. Sci. Appl., 17 (2007), 225-237. |
[8] |
R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics," Second edition, Applied Mathematical Sciences, 68, Springer-Verlag, New York, 1997. |
[9] |
C.-K. Zhong, M.-H. Yang and C.-Y. Sun, The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations, J. Differential Equations, 223 (2006), 367-399.
doi: 10.1016/j.jde.2005.06.008. |
show all references
References:
[1] |
A. V. Babin and M. I. Vishik, "Attractors of Evolution Equations," Studies in Mathematics and its Applications, 25, North-Holland Publishing Co., Amsterdam, 1992. |
[2] |
V. V. Chepyzhov and M. I. Vishik, "Attractors for Equations of Mathematical Physics,'' American Mathematical Society Colloquium Publications, 49, American Mathematical Society, Providence, RI, 2002. |
[3] |
J. K. Hale, "Asymptotic Behavior of Dissipative Systems," Mathematical Surveys and Monographs, 25, American Mathematical Society, Providence, RI, 1988. |
[4] |
A. Haraux, "Systèmes Dynamiques Dissipatifs et Applications," Recherches en Mathématiques Appliquées, 17, Masson, Paris, 1991. |
[5] |
A. Miranville and S. Zelik, Attractors for dissipative partial differential equations in bounded and unbounded domains, in "Handbook of Differential Equations: Evolutionary Equations," Vol. IV, Elsevier/North-Holland, Amsterdam, (2008), 103-200. |
[6] |
V. Pata and S. Zelik, A result on the existence of global attractors for semigroups of closed operators, Commun. Pure Appl. Anal., 6 (2007), 481-486.
doi: 10.3934/cpaa.2007.6.481. |
[7] |
V. Pata and S. Zelik, Attractors and their regularity for 2-D wave equation with nonlinear damping, Adv. Math. Sci. Appl., 17 (2007), 225-237. |
[8] |
R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics," Second edition, Applied Mathematical Sciences, 68, Springer-Verlag, New York, 1997. |
[9] |
C.-K. Zhong, M.-H. Yang and C.-Y. Sun, The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations, J. Differential Equations, 223 (2006), 367-399.
doi: 10.1016/j.jde.2005.06.008. |
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