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Recurrent equations with sign and Fredholm alternative
Structure of the pullback attractor for a non-autonomous scalar differential inclusion
1. | Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain, Spain |
2. | Centro de Investigación Operativa, Universidad Miguel Hernández, Avda. Universidad, s/n, 03202-Elche, Spain |
References:
[1] |
J. Ball, On the asymptotic behavior of generalized processes with applications to nonlinear evolution equations,, J. Differential Equations, 27 (1978), 224.
doi: 10.1016/0022-0396(78)90032-3. |
[2] |
E. Capelato and J. Simsen, Some properties for exact generalized processes,, in Continuous and Distributed Systems II (V.A Zadovnichiy and M.Z. Zgurovsky eds.), 30 (2015), 209.
doi: 10.1007/978-3-319-19075-4_12. |
[3] |
T. Caraballo, J. A. Langa and J. Valero, Asymptotic behaviour of monotone multi-valued dynamical systems,, Dyn. System: An Int. J., 20 (2005), 301.
doi: 10.1080/14689360500151847. |
[4] |
T. Caraballo, J. A. Langa, V. S. Melnik and J. Valero, Pullback attractors of nonautonomous and stochastic multivalued dynamical systems,, Set-Valued Anal., 11 (2003), 153.
doi: 10.1023/A:1022902802385. |
[5] |
A. N. Carvalho, J. A. Langa and J. C. Robinson, Attractors for Infinite-Dimensional Nonautonomous Dynamical Systems,, Springer, (2013).
doi: 10.1007/978-1-4614-4581-4. |
[6] |
T. Caraballo, P. Marín-Rubio and J. C. Robinson, A comparison between two theories for multivalued semiflows and their asymptotic behaviour,, Set-Valued Anal., 11 (2003), 297.
doi: 10.1023/A:1024422619616. |
[7] |
M. Coti Zelati and P. Kalita, Minimality properties of set-valued processes and their pullback attractors,, SIAM J. Math. Anal., 47 (2015), 1530.
doi: 10.1137/140978995. |
[8] |
M. O. Gluzman, N. V. Gorban and P. O. Kasyanov, Lyapunov type functions for classes of autonomous parabolic feedback control problems and applications,, Appl. Math. Lett., 39 (2015), 19.
doi: 10.1016/j.aml.2014.08.006. |
[9] |
O. V. Kapustyan, P. O. Kasyanov and J. Valero, Pullback attractors for a class of extremal solutions of the 3D Navier-Stokes system,, J. Math. Anal. Appl., 373 (2011), 535.
doi: 10.1016/j.jmaa.2010.07.040. |
[10] |
O. V. Kapustyan, O. P. Kasyanov and J. Valero, Structure and regularity of the global attractor of a reaction-diffusion equation with non-smooth nonlinear term,, Discrete and Continuous Dynamical Systems, 34 (2014), 4155.
doi: 10.3934/dcds.2014.34.4155. |
[11] |
P. O. Kasyanov, L. Toscano and N. V. Zadoianchuk, Regularity of weak solutions and their attractors for a parabolic feeback control problem,, Set-Valued Var. Anal., 21 (2013), 271.
doi: 10.1007/s11228-013-0233-8. |
[12] |
J. A. Langa, J. C. Robinson and A. Suarez, Stability, instability, and bifurcation phenomena in nonautonomous differential equations,, Nonlinearity, 15 (2002), 887.
doi: 10.1088/0951-7715/15/3/322. |
[13] |
V. S. Melnik and J. Valero, On attractors of multi-valued semi-flows and differential inclusions,, Set-Valued Anal., 6 (1998), 83.
doi: 10.1023/A:1008608431399. |
[14] |
A. Rodrígez-Bernal and A. Vidal-López, Existence, uniqueness and attractivity properties of positive complete trajectories for nonautonomous reaction-diffusion problems,, Discrete and Continuous Dynamical Systems, 18 (2007), 537.
doi: 10.3934/dcds.2007.18.537. |
[15] |
M. Z. Zgurovsky and P. O. Kasyanov, Evolution inclusions in nonsmooth systems with applications for earth data processing: uniform trajectory attractors for nonautonomous evolution inclusions solutions with pointwise pseudomonotone mappings,, in Advances in global optimization, 95 (2015), 283.
doi: 10.1007/978-3-319-08377-3_28. |
[16] |
M. Z. Zgurovsky, P. O. Kasyanov, O. V. Kapustyan, J. Valero and N. V. Zadoianchuk, Evolution Inclusions and Variation Inequalities for Earth Data Processing III,, Springer, (2012).
doi: 10.1007/978-3-642-28512-7. |
show all references
References:
[1] |
J. Ball, On the asymptotic behavior of generalized processes with applications to nonlinear evolution equations,, J. Differential Equations, 27 (1978), 224.
doi: 10.1016/0022-0396(78)90032-3. |
[2] |
E. Capelato and J. Simsen, Some properties for exact generalized processes,, in Continuous and Distributed Systems II (V.A Zadovnichiy and M.Z. Zgurovsky eds.), 30 (2015), 209.
doi: 10.1007/978-3-319-19075-4_12. |
[3] |
T. Caraballo, J. A. Langa and J. Valero, Asymptotic behaviour of monotone multi-valued dynamical systems,, Dyn. System: An Int. J., 20 (2005), 301.
doi: 10.1080/14689360500151847. |
[4] |
T. Caraballo, J. A. Langa, V. S. Melnik and J. Valero, Pullback attractors of nonautonomous and stochastic multivalued dynamical systems,, Set-Valued Anal., 11 (2003), 153.
doi: 10.1023/A:1022902802385. |
[5] |
A. N. Carvalho, J. A. Langa and J. C. Robinson, Attractors for Infinite-Dimensional Nonautonomous Dynamical Systems,, Springer, (2013).
doi: 10.1007/978-1-4614-4581-4. |
[6] |
T. Caraballo, P. Marín-Rubio and J. C. Robinson, A comparison between two theories for multivalued semiflows and their asymptotic behaviour,, Set-Valued Anal., 11 (2003), 297.
doi: 10.1023/A:1024422619616. |
[7] |
M. Coti Zelati and P. Kalita, Minimality properties of set-valued processes and their pullback attractors,, SIAM J. Math. Anal., 47 (2015), 1530.
doi: 10.1137/140978995. |
[8] |
M. O. Gluzman, N. V. Gorban and P. O. Kasyanov, Lyapunov type functions for classes of autonomous parabolic feedback control problems and applications,, Appl. Math. Lett., 39 (2015), 19.
doi: 10.1016/j.aml.2014.08.006. |
[9] |
O. V. Kapustyan, P. O. Kasyanov and J. Valero, Pullback attractors for a class of extremal solutions of the 3D Navier-Stokes system,, J. Math. Anal. Appl., 373 (2011), 535.
doi: 10.1016/j.jmaa.2010.07.040. |
[10] |
O. V. Kapustyan, O. P. Kasyanov and J. Valero, Structure and regularity of the global attractor of a reaction-diffusion equation with non-smooth nonlinear term,, Discrete and Continuous Dynamical Systems, 34 (2014), 4155.
doi: 10.3934/dcds.2014.34.4155. |
[11] |
P. O. Kasyanov, L. Toscano and N. V. Zadoianchuk, Regularity of weak solutions and their attractors for a parabolic feeback control problem,, Set-Valued Var. Anal., 21 (2013), 271.
doi: 10.1007/s11228-013-0233-8. |
[12] |
J. A. Langa, J. C. Robinson and A. Suarez, Stability, instability, and bifurcation phenomena in nonautonomous differential equations,, Nonlinearity, 15 (2002), 887.
doi: 10.1088/0951-7715/15/3/322. |
[13] |
V. S. Melnik and J. Valero, On attractors of multi-valued semi-flows and differential inclusions,, Set-Valued Anal., 6 (1998), 83.
doi: 10.1023/A:1008608431399. |
[14] |
A. Rodrígez-Bernal and A. Vidal-López, Existence, uniqueness and attractivity properties of positive complete trajectories for nonautonomous reaction-diffusion problems,, Discrete and Continuous Dynamical Systems, 18 (2007), 537.
doi: 10.3934/dcds.2007.18.537. |
[15] |
M. Z. Zgurovsky and P. O. Kasyanov, Evolution inclusions in nonsmooth systems with applications for earth data processing: uniform trajectory attractors for nonautonomous evolution inclusions solutions with pointwise pseudomonotone mappings,, in Advances in global optimization, 95 (2015), 283.
doi: 10.1007/978-3-319-08377-3_28. |
[16] |
M. Z. Zgurovsky, P. O. Kasyanov, O. V. Kapustyan, J. Valero and N. V. Zadoianchuk, Evolution Inclusions and Variation Inequalities for Earth Data Processing III,, Springer, (2012).
doi: 10.1007/978-3-642-28512-7. |
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