# American Institute of Mathematical Sciences

• Previous Article
Global attractors for weak solutions of the three-dimensional Navier-Stokes equations with damping
• DCDS-B Home
• This Issue
• Next Article
Minimax joint spectral radius and stabilizability of discrete-time linear switching control systems
August  2019, 24(8): 3557-3567. doi: 10.3934/dcdsb.2018278

## On asymptotically autonomous dynamics for multivalued evolution problems

 Instituto de Matemática e Computação, Universidade Federal de Itajubá, 37500-903 - Itajubá - Minas Gerais, Brazil

* Corresponding author: Jacson Simsen, jacson@unifei.edu.br

Dedicated to Peter E. Kloeden on occasion of his 70th birthday

Received  February 2018 Revised  June 2018 Published  October 2018

Fund Project: This work has been partially supported by FAPEMIG (Brazil) - processes PPM 00329-16 and CEX-APQ-00814-16.

In this work we improve the result presented by Kloeden-Simsen-Stefanello Simsen in [8] by reducing uniform conditions. We prove theoretical results in order to establish convergence in the Hausdorff semi-distance of the component subsets of the pullback attractor of a non-autonomous multivalued problem to the global attractor of the corresponding autonomous multivalued problem.

Citation: Jacson Simsen, Mariza Stefanello Simsen. On asymptotically autonomous dynamics for multivalued evolution problems. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3557-3567. doi: 10.3934/dcdsb.2018278
##### References:

show all references

##### References:
 [1] Peter E. Kloeden, Jacson Simsen. Pullback attractors for non-autonomous evolution equations with spatially variable exponents. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2543-2557. doi: 10.3934/cpaa.2014.13.2543 [2] Hongyong Cui. Convergences of asymptotically autonomous pullback attractors towards semigroup attractors. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3525-3535. doi: 10.3934/dcdsb.2018276 [3] Ting Li. Pullback attractors for asymptotically upper semicompact non-autonomous multi-valued semiflows. Communications on Pure & Applied Analysis, 2007, 6 (1) : 279-285. doi: 10.3934/cpaa.2007.6.279 [4] Jong Yeoul Park, Jae Ug Jeong. Pullback attractors for a $2D$-non-autonomous incompressible non-Newtonian fluid with variable delays. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2687-2702. doi: 10.3934/dcdsb.2016068 [5] Mohamed Ali Hammami, Lassaad Mchiri, Sana Netchaoui, Stefanie Sonner. Pullback exponential attractors for differential equations with variable delays. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 301-319. doi: 10.3934/dcdsb.2019183 [6] Mirelson M. Freitas, Alberto L. C. Costa, Geraldo M. Araújo. Pullback dynamics of a non-autonomous mixture problem in one dimensional solids with nonlinear damping. Communications on Pure & Applied Analysis, 2020, 19 (2) : 785-809. doi: 10.3934/cpaa.2020037 [7] Flank D. M. Bezerra, Vera L. Carbone, Marcelo J. D. Nascimento, Karina Schiabel. Pullback attractors for a class of non-autonomous thermoelastic plate systems. Discrete & Continuous Dynamical Systems - B, 2018, 23 (9) : 3553-3571. doi: 10.3934/dcdsb.2017214 [8] Zhijian Yang, Yanan Li. Upper semicontinuity of pullback attractors for non-autonomous Kirchhoff wave equations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (9) : 4899-4912. doi: 10.3934/dcdsb.2019036 [9] Noriaki Yamazaki. Global attractors for non-autonomous multivalued dynamical systems associated with double obstacle problems. Conference Publications, 2003, 2003 (Special) : 935-944. doi: 10.3934/proc.2003.2003.935 [10] Rodrigo Samprogna, Tomás Caraballo. Pullback attractor for a dynamic boundary non-autonomous problem with Infinite Delay. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 509-523. doi: 10.3934/dcdsb.2017195 [11] Antonio Carlos Fernandes, Marcela Carvalho Gonçcalves, Jacson Simsen. Non-autonomous reaction-diffusion equations with variable exponents and large diffusion. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1485-1510. doi: 10.3934/dcdsb.2018217 [12] Zhijian Yang, Yanan Li. Criteria on the existence and stability of pullback exponential attractors and their application to non-autonomous kirchhoff wave models. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2629-2653. doi: 10.3934/dcds.2018111 [13] Xue-Li Song, Yan-Ren Hou. Pullback $\mathcal{D}$-attractors for the non-autonomous Newton-Boussinesq equation in two-dimensional bounded domain. Discrete & Continuous Dynamical Systems - A, 2012, 32 (3) : 991-1009. doi: 10.3934/dcds.2012.32.991 [14] Julia García-Luengo, Pedro Marín-Rubio, José Real, James C. Robinson. Pullback attractors for the non-autonomous 2D Navier--Stokes equations for minimally regular forcing. Discrete & Continuous Dynamical Systems - A, 2014, 34 (1) : 203-227. doi: 10.3934/dcds.2014.34.203 [15] Bo You, Chengkui Zhong, Fang Li. Pullback attractors for three dimensional non-autonomous planetary geostrophic viscous equations of large-scale ocean circulation. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 1213-1226. doi: 10.3934/dcdsb.2014.19.1213 [16] Fang Li, Bo You. Pullback exponential attractors for the three dimensional non-autonomous Navier-Stokes equations with nonlinear damping. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 55-80. doi: 10.3934/dcdsb.2019172 [17] Lu Yang, Meihua Yang, Peter E. Kloeden. Pullback attractors for non-autonomous quasi-linear parabolic equations with dynamical boundary conditions. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2635-2651. doi: 10.3934/dcdsb.2012.17.2635 [18] Suping Wang, Qiaozhen Ma. Existence of pullback attractors for the non-autonomous suspension bridge equation with time delay. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1299-1316. doi: 10.3934/dcdsb.2019221 [19] Bo You, Yanren Hou, Fang Li, Jinping Jiang. Pullback attractors for the non-autonomous quasi-linear complex Ginzburg-Landau equation with $p$-Laplacian. Discrete & Continuous Dynamical Systems - B, 2014, 19 (6) : 1801-1814. doi: 10.3934/dcdsb.2014.19.1801 [20] Svetlana Pastukhova, Valeria Chiadò Piat. Homogenization of multivalued monotone operators with variable growth exponent. Networks & Heterogeneous Media, 2020, 15 (2) : 281-305. doi: 10.3934/nhm.2020013

2019 Impact Factor: 1.27