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Asymptotic behaviour of a non-autonomous Lorenz-84 system
Estimates on the distance of inertial manifolds
1. | Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain, Spain |
References:
[1] |
J. M. Arrieta and A. N. Carvalho, Spectral convergence and nonlinear dynamics of reaction-diffusion equations under perturbations of the domain, Journal of Differential Equations, 199 (2004), 143-178.
doi: 10.1016/j.jde.2003.09.004. |
[2] |
J. M. Arrieta, A. N. Carvalho and G. Lozada-Cruz, Dynamics in dumbbell domains I. continuity of the set of equilibria, Journal of Differential Equations, 231 (2006).
doi: 10.1016/j.jde.2006.06.002. |
[3] |
J. M. Arrieta, A. N. Carvalho and G. Lozada-Cruz, Dynamics in Dumbbell Domains III. Continuity of attractors, Journal of Differential Equations, 247 (2009), 225-259.
doi: 10.1016/j.jde.2008.12.014. |
[4] |
J. M. Arrieta and E. Santamaría, Distance of attractors for thin domains, in preparation. |
[5] |
A. V. Babin and M. I. Vishik, Attractors of Evolution Equations, Studies in Mathematics and its Applications, 25, North-Holland Publishing Co., Amsterdam, 1992. |
[6] |
P. W. Bates, K. Lu and C. Zeng, Existence and persistence of invariant manifolds for semiflows in banach space, Mem. Am. Math. Soc., 135 (1998).
doi: 10.1090/memo/0645. |
[7] |
A. N. Carvalho, J. Langa and J. C. Robinson, Attractors for Infinite-Dimensional Non-Autonomous Dynamical-Systems, Applied Mathematical Sciences, 182, Springer, 2012.
doi: 10.1007/978-1-4614-4581-4. |
[8] |
A. N. Carvalho and S. Piskarev, A general approximation scheme for attractors of abstract parabolic problems, Numerical Functional Analysis and Optimization, 27 (2006), 785-829.
doi: 10.1080/01630560600882723. |
[9] |
S.-N. Chow, X.-B. Lin and K. Lu, Smooth invariant foliations in infinite dimensional spaces, Journal of Differential Equations, 94 (1991), 266-291.
doi: 10.1016/0022-0396(91)90093-O. |
[10] |
S.-N. Chow, K. Lu and G. R. Sell, Smoothness of inertial manifolds, Journal of Mathematical Analysis and Applications, 169 (1992), 283-312.
doi: 10.1016/0022-247X(92)90115-T. |
[11] |
J. W. Cholewa and T. Dlotko, Global Attractors in Abstract Parabolic Problems, London Mathematical Society Lecture Note Series, 278, Cambridge University Press, Cambridge, 2000.
doi: 10.1017/CBO9780511526404. |
[12] |
J. K. Hale, Asymptotic Behavior of Dissipative Systems, American Mathematical Society, 1988. |
[13] |
J. K. Hale and G. Raugel, Reaction-Diffusion Equation on Thin Domains, J. Math. Pures et Appl., 71 (1992), 33-95. |
[14] |
D. B. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, 840, Springer-Verlag, Berlin-New York, 1981. |
[15] |
D. A. Jones, A. M. Stuart and E. S. Titi, Persistence of invariant sets for dissipative evolution equations, Journal of Mathematical Analysis and Applications, 219 (1998), 479-502.
doi: 10.1006/jmaa.1997.5847. |
[16] |
P. S. Ngiamsunthorn, Invariant manifolds for parabolic equations under perturbation of the domain, Nonlinear Analysis TMA, 80 (2013), 23-48.
doi: 10.1016/j.na.2012.12.001. |
[17] |
G. Raugel, Dynamics of partial differential equations on thin domains, in Dynamical Systems (Montecatini Terme, 1994), Lecture Notes in Math., 1609, Springer, Berlin, 1995, 208-315.
doi: 10.1007/BFb0095241. |
[18] |
J. C. Robinson, Infinite-Dimensional Dynamical Systems. An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors, Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, 2001. |
[19] |
G. R. Sell and Y. You, Dynamics of Evolutionary Equations, Applied Mathematical Sciences, 143, Springer, 2002. |
[20] |
N. Varchon, Domain perturbation and invariant manifolds, J. Evol. Equ., 12 (2012), 547-569.
doi: 10.1007/s00028-012-0144-4. |
show all references
References:
[1] |
J. M. Arrieta and A. N. Carvalho, Spectral convergence and nonlinear dynamics of reaction-diffusion equations under perturbations of the domain, Journal of Differential Equations, 199 (2004), 143-178.
doi: 10.1016/j.jde.2003.09.004. |
[2] |
J. M. Arrieta, A. N. Carvalho and G. Lozada-Cruz, Dynamics in dumbbell domains I. continuity of the set of equilibria, Journal of Differential Equations, 231 (2006).
doi: 10.1016/j.jde.2006.06.002. |
[3] |
J. M. Arrieta, A. N. Carvalho and G. Lozada-Cruz, Dynamics in Dumbbell Domains III. Continuity of attractors, Journal of Differential Equations, 247 (2009), 225-259.
doi: 10.1016/j.jde.2008.12.014. |
[4] |
J. M. Arrieta and E. Santamaría, Distance of attractors for thin domains, in preparation. |
[5] |
A. V. Babin and M. I. Vishik, Attractors of Evolution Equations, Studies in Mathematics and its Applications, 25, North-Holland Publishing Co., Amsterdam, 1992. |
[6] |
P. W. Bates, K. Lu and C. Zeng, Existence and persistence of invariant manifolds for semiflows in banach space, Mem. Am. Math. Soc., 135 (1998).
doi: 10.1090/memo/0645. |
[7] |
A. N. Carvalho, J. Langa and J. C. Robinson, Attractors for Infinite-Dimensional Non-Autonomous Dynamical-Systems, Applied Mathematical Sciences, 182, Springer, 2012.
doi: 10.1007/978-1-4614-4581-4. |
[8] |
A. N. Carvalho and S. Piskarev, A general approximation scheme for attractors of abstract parabolic problems, Numerical Functional Analysis and Optimization, 27 (2006), 785-829.
doi: 10.1080/01630560600882723. |
[9] |
S.-N. Chow, X.-B. Lin and K. Lu, Smooth invariant foliations in infinite dimensional spaces, Journal of Differential Equations, 94 (1991), 266-291.
doi: 10.1016/0022-0396(91)90093-O. |
[10] |
S.-N. Chow, K. Lu and G. R. Sell, Smoothness of inertial manifolds, Journal of Mathematical Analysis and Applications, 169 (1992), 283-312.
doi: 10.1016/0022-247X(92)90115-T. |
[11] |
J. W. Cholewa and T. Dlotko, Global Attractors in Abstract Parabolic Problems, London Mathematical Society Lecture Note Series, 278, Cambridge University Press, Cambridge, 2000.
doi: 10.1017/CBO9780511526404. |
[12] |
J. K. Hale, Asymptotic Behavior of Dissipative Systems, American Mathematical Society, 1988. |
[13] |
J. K. Hale and G. Raugel, Reaction-Diffusion Equation on Thin Domains, J. Math. Pures et Appl., 71 (1992), 33-95. |
[14] |
D. B. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, 840, Springer-Verlag, Berlin-New York, 1981. |
[15] |
D. A. Jones, A. M. Stuart and E. S. Titi, Persistence of invariant sets for dissipative evolution equations, Journal of Mathematical Analysis and Applications, 219 (1998), 479-502.
doi: 10.1006/jmaa.1997.5847. |
[16] |
P. S. Ngiamsunthorn, Invariant manifolds for parabolic equations under perturbation of the domain, Nonlinear Analysis TMA, 80 (2013), 23-48.
doi: 10.1016/j.na.2012.12.001. |
[17] |
G. Raugel, Dynamics of partial differential equations on thin domains, in Dynamical Systems (Montecatini Terme, 1994), Lecture Notes in Math., 1609, Springer, Berlin, 1995, 208-315.
doi: 10.1007/BFb0095241. |
[18] |
J. C. Robinson, Infinite-Dimensional Dynamical Systems. An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors, Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, 2001. |
[19] |
G. R. Sell and Y. You, Dynamics of Evolutionary Equations, Applied Mathematical Sciences, 143, Springer, 2002. |
[20] |
N. Varchon, Domain perturbation and invariant manifolds, J. Evol. Equ., 12 (2012), 547-569.
doi: 10.1007/s00028-012-0144-4. |
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