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Inertial manifolds for a class of non-autonomous semilinear parabolic equations with finite delay
1. | Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam |
2. | The Academy of Journalism and Communication, 36 Xuan Thuy, Cau Giay, Hanoi, Vietnam |
3. | School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Vien Toan ung dung va Tin hoc, Dai hoc Bach khoa Hanoi, 1 Dai Co Viet, Hanoi, Vietnam |
References:
[1] |
A. Bensoussan and F. Landoli, Stochastic inertial manifolds, Stochastics Rep., 53 (1995), 13-39. |
[2] |
L. Boutet de Monvel, I. D. Chueshov and A. V. Rezounenko, Inertial manifolds for retarded semilinear parabolic equations, Nonlinear Anal., 34 (1998), 907-925.
doi: 10.1016/S0362-546X(97)00569-5. |
[3] |
A. P. Calderon, Spaces between $L^1$ and $L^\infty$ and the theorem of Marcinkiewicz, Studia Math, 26 (1996), 273-299. |
[4] |
T. Caraballo and J. A. Langa, Tracking properties of trajectories on random attracting sets, Stochastic Anal. Appl., 17 (1999), 339-358.
doi: 10.1080/07362999908809605. |
[5] |
I. D. Chueshov, Approximate inertial manifolds of exponential order for semilinear parabolic equations subjected to additive white noise, J. Dyn. Differ. Equations, 7 (1995), 549-566. |
[6] |
I. D. Chueshov, "Introduction to the Theory of Infinite-Dimensional Dissipative Systems," Acta, 2002. |
[7] |
I. D. Chueshov and M. Scheutzow, Inertial manifolds and forms for stochastically perturbed retarded semilinear parabolic equations, J. Dyn. Differ. Equations, 13 (2001), 355-380. |
[8] |
C. Foias, G. R. Sell and R. Temam, Inertial manifolds for nonlinear evolutionary equations, J. Differ. Equations, 73 (1988), 309-353.
doi: 10.1016/0022-0396(88)90110-6. |
[9] |
A. Y. Goritskij and M. I. Vishik, Local integral manifolds for a nonautonomous parabolic equation, J. Math. Sci., 85 (1997), 2428-2439.
doi: 10.1007/BF02355848. |
[10] |
N. T. Huy, Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line, J. Funct. Anal., 235 (2006), 330-354.
doi: 10.1016/j.jfa.2005.11.002. |
[11] |
N. T. Huy, Inertial manifolds for semilinear parabolic equations in admissible spaces, J. Math. Anal. Appl., 386 (2012), 894-909.
doi: 10.1016/j.jmaa.2011.08.051. |
[12] |
N. Koksch and S. Siegmund, Pullback attracting inertial manifols for nonautonomous dynamical systems, J. Dyn. Differ. Equations, 14 (2002), 889-941. |
[13] |
Y. Latushkin and B. Layton, The optimal gap condition for invariant manifolds, Discrete and Continuous Dynamical System, 5 (1999), 233-268.
doi: 10.3934/dcds.1999.5.233. |
[14] |
J. Lindenstrauss and L. Tzafriri, "Classical Banach Spaces II, Function Spaces," Springer-Verlag, Berlin, 1979. |
[15] |
J. J. Massera and J. J. Schäffer, "Linear Differential Equations and Function Spaces," Academic Press, New York, 1966. |
[16] |
M. Taboado and Y. You, Invariant manifolds for retarded semilinear wave equations, J. Differ. Equations, 114 (1994), 337-369.
doi: 10.1006/jdeq.1994.1153. |
[17] |
G. R. Sell and Y. You, "Dynamics of Evolutionary Equations," Springer, 2002. |
[18] |
R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics," 2nd edition, Springer, 1997. |
show all references
References:
[1] |
A. Bensoussan and F. Landoli, Stochastic inertial manifolds, Stochastics Rep., 53 (1995), 13-39. |
[2] |
L. Boutet de Monvel, I. D. Chueshov and A. V. Rezounenko, Inertial manifolds for retarded semilinear parabolic equations, Nonlinear Anal., 34 (1998), 907-925.
doi: 10.1016/S0362-546X(97)00569-5. |
[3] |
A. P. Calderon, Spaces between $L^1$ and $L^\infty$ and the theorem of Marcinkiewicz, Studia Math, 26 (1996), 273-299. |
[4] |
T. Caraballo and J. A. Langa, Tracking properties of trajectories on random attracting sets, Stochastic Anal. Appl., 17 (1999), 339-358.
doi: 10.1080/07362999908809605. |
[5] |
I. D. Chueshov, Approximate inertial manifolds of exponential order for semilinear parabolic equations subjected to additive white noise, J. Dyn. Differ. Equations, 7 (1995), 549-566. |
[6] |
I. D. Chueshov, "Introduction to the Theory of Infinite-Dimensional Dissipative Systems," Acta, 2002. |
[7] |
I. D. Chueshov and M. Scheutzow, Inertial manifolds and forms for stochastically perturbed retarded semilinear parabolic equations, J. Dyn. Differ. Equations, 13 (2001), 355-380. |
[8] |
C. Foias, G. R. Sell and R. Temam, Inertial manifolds for nonlinear evolutionary equations, J. Differ. Equations, 73 (1988), 309-353.
doi: 10.1016/0022-0396(88)90110-6. |
[9] |
A. Y. Goritskij and M. I. Vishik, Local integral manifolds for a nonautonomous parabolic equation, J. Math. Sci., 85 (1997), 2428-2439.
doi: 10.1007/BF02355848. |
[10] |
N. T. Huy, Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line, J. Funct. Anal., 235 (2006), 330-354.
doi: 10.1016/j.jfa.2005.11.002. |
[11] |
N. T. Huy, Inertial manifolds for semilinear parabolic equations in admissible spaces, J. Math. Anal. Appl., 386 (2012), 894-909.
doi: 10.1016/j.jmaa.2011.08.051. |
[12] |
N. Koksch and S. Siegmund, Pullback attracting inertial manifols for nonautonomous dynamical systems, J. Dyn. Differ. Equations, 14 (2002), 889-941. |
[13] |
Y. Latushkin and B. Layton, The optimal gap condition for invariant manifolds, Discrete and Continuous Dynamical System, 5 (1999), 233-268.
doi: 10.3934/dcds.1999.5.233. |
[14] |
J. Lindenstrauss and L. Tzafriri, "Classical Banach Spaces II, Function Spaces," Springer-Verlag, Berlin, 1979. |
[15] |
J. J. Massera and J. J. Schäffer, "Linear Differential Equations and Function Spaces," Academic Press, New York, 1966. |
[16] |
M. Taboado and Y. You, Invariant manifolds for retarded semilinear wave equations, J. Differ. Equations, 114 (1994), 337-369.
doi: 10.1006/jdeq.1994.1153. |
[17] |
G. R. Sell and Y. You, "Dynamics of Evolutionary Equations," Springer, 2002. |
[18] |
R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics," 2nd edition, Springer, 1997. |
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