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Asymptotic behavior of the conserved Caginalp phase-field system based on the Maxwell-Cattaneo law
Totally dissipative dynamical processes and their uniform global attractors
1. | Institute for Information Transmission Problems, Russian Academy of Sciences, Bolshoy Karetniy 19, Moscow 101447 |
2. | Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano |
References:
[1] |
A. V. Babin and M. I. Vishik, Attractors of Evolution Equations, North-Holland, Amsterdam, 1992. |
[2] |
V. V. Chepyzhov, M. Conti and V. Pata, A minimal approach to the theory of global attractors, Discrete Contin. Dynam. Systems, 32 (2012), 2079-2088.
doi: 10.3934/dcds.2012.32.2079. |
[3] |
V. V. Chepyzhov and M. I. Vishik, Nonautonomous evolution equations and their attractors, Russian J. Math. Phys., 1 (1993), 165-190. |
[4] |
V. V. Chepyzhov and M. I. Vishik, Attractors of nonautonomous dynamical systems and their dimension, J. Math. Pures Appl., 73 (1994), 279-333. |
[5] |
V. V. Chepyzhov and M. I. Vishik, Periodic processes and non-autonomous evolution equations with time-periodic terms, Topol. Methods Nonlinear Anal., 4 (1994), 1-17. |
[6] |
V. V. Chepyzhov and M. I. Vishik, Attractors of periodic processes and estimates of their dimensions, Math. Notes, 57 (1995), 127-140.
doi: 10.1007/BF02309145. |
[7] |
V. V. Chepyzhov and M. I. Vishik, Attractors for Equations of Mathematical Physics, American Mathematical Society, Providence, 2002. |
[8] |
S. Gatti and V. Pata, A one-dimensional wave equation with nonlinear damping, Glasg. Math. J., 48 (2006), 419-430.
doi: 10.1017/S0017089506003156. |
[9] |
J. K. Hale, Asymptotic Behavior of Dissipative Systems, American Mathematical Society, Providence, 1988. |
[10] |
A. Haraux, Systèmes dynamiques dissipatifs et applications, Coll. RMA no.17, Masson, Paris, 1991. |
[11] |
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. |
[12] |
G. R. Sell and Y. You, Dynamics of Evolutionary Equations, Springer-Verlag, New York, 2002.
doi: 10.1007/978-1-4757-5037-9. |
[13] |
R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, Springer, New York, 1997.
doi: 10.1007/978-1-4612-0645-3. |
show all references
References:
[1] |
A. V. Babin and M. I. Vishik, Attractors of Evolution Equations, North-Holland, Amsterdam, 1992. |
[2] |
V. V. Chepyzhov, M. Conti and V. Pata, A minimal approach to the theory of global attractors, Discrete Contin. Dynam. Systems, 32 (2012), 2079-2088.
doi: 10.3934/dcds.2012.32.2079. |
[3] |
V. V. Chepyzhov and M. I. Vishik, Nonautonomous evolution equations and their attractors, Russian J. Math. Phys., 1 (1993), 165-190. |
[4] |
V. V. Chepyzhov and M. I. Vishik, Attractors of nonautonomous dynamical systems and their dimension, J. Math. Pures Appl., 73 (1994), 279-333. |
[5] |
V. V. Chepyzhov and M. I. Vishik, Periodic processes and non-autonomous evolution equations with time-periodic terms, Topol. Methods Nonlinear Anal., 4 (1994), 1-17. |
[6] |
V. V. Chepyzhov and M. I. Vishik, Attractors of periodic processes and estimates of their dimensions, Math. Notes, 57 (1995), 127-140.
doi: 10.1007/BF02309145. |
[7] |
V. V. Chepyzhov and M. I. Vishik, Attractors for Equations of Mathematical Physics, American Mathematical Society, Providence, 2002. |
[8] |
S. Gatti and V. Pata, A one-dimensional wave equation with nonlinear damping, Glasg. Math. J., 48 (2006), 419-430.
doi: 10.1017/S0017089506003156. |
[9] |
J. K. Hale, Asymptotic Behavior of Dissipative Systems, American Mathematical Society, Providence, 1988. |
[10] |
A. Haraux, Systèmes dynamiques dissipatifs et applications, Coll. RMA no.17, Masson, Paris, 1991. |
[11] |
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. |
[12] |
G. R. Sell and Y. You, Dynamics of Evolutionary Equations, Springer-Verlag, New York, 2002.
doi: 10.1007/978-1-4757-5037-9. |
[13] |
R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, Springer, New York, 1997.
doi: 10.1007/978-1-4612-0645-3. |
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