American Institute of Mathematical Sciences

Advanced
2003, 2003(Special): 935-944. doi: 10.3934/proc.2003.2003.935

Global attractors for non-autonomous multivalued dynamical systems associated with double obstacle problems

Noriaki Yamazaki 1,

1. 

Department of Mathematical Science, Common Subject Division, Muroran Institute of Technology, 27-1 Mizumoto-chō, Muroran

Received  August 2002 Published  April 2003

In this paper we consider double obstacle problems including regional economic growth models. Unfortunately, by prescribed double obstacles, our problems lose the uniqueness of solutions. So, our problems have multiple solutions for a given initial value. Hence, the associated dynamical systems are multivalued. In this paper we shall consider the large-time behaviour of multiple solutions from the viewpoint of attractors. Namely, the main object of this paper is to construct the global attractors for non-autonomous multivalued dynamical systems associated with double obstacle problems.
Keywords: multivalued dynamical systems, obstacle problems., Attractor.
Mathematics Subject Classification: 35B35, 35B40, 35K5.
Citation: 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
[1]

Rubén Caballero, Alexandre N. Carvalho, Pedro Marín-Rubio, José Valero. Robustness of dynamically gradient multivalued dynamical systems. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 1049-1077. doi: 10.3934/dcdsb.2019006
[2]

María J. Garrido-Atienza, Oleksiy V. Kapustyan, José Valero. Preface to the special issue "Finite and infinite dimensional multivalued dynamical systems". Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : i-iv. doi: 10.3934/dcdsb.201705i
[3]

Bixiang Wang. Multivalued non-autonomous random dynamical systems for wave equations without uniqueness. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 2011-2051. doi: 10.3934/dcdsb.2017119
[4]

Tomás Caraballo, David Cheban. On the structure of the global attractor for non-autonomous dynamical systems with weak convergence. Communications on Pure & Applied Analysis, 2012, 11 (2) : 809-828. doi: 10.3934/cpaa.2012.11.809
[5]

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
[6]

Alexandre N. Carvalho, José A. Langa, James C. Robinson. Forwards dynamics of non-autonomous dynamical systems: Driving semigroups without backwards uniqueness and structure of the attractor. Communications on Pure & Applied Analysis, 2020, 19 (4) : 1997-2013. doi: 10.3934/cpaa.2020088
[7]

Tomás Caraballo, David Cheban. On the structure of the global attractor for infinite-dimensional non-autonomous dynamical systems with weak convergence. Communications on Pure & Applied Analysis, 2013, 12 (1) : 281-302. doi: 10.3934/cpaa.2013.12.281
[8]

Luis Caffarelli, Antoine Mellet. Random homogenization of fractional obstacle problems. Networks & Heterogeneous Media, 2008, 3 (3) : 523-554. doi: 10.3934/nhm.2008.3.523
[9]

Tan Bui-Thanh, Omar Ghattas. Analysis of the Hessian for inverse scattering problems. Part III: Inverse medium scattering of electromagnetic waves in three dimensions. Inverse Problems & Imaging, 2013, 7 (4) : 1139-1155. doi: 10.3934/ipi.2013.7.1139
[10]

Sari Lasanen. Non-Gaussian statistical inverse problems. Part II: Posterior convergence for approximated unknowns. Inverse Problems & Imaging, 2012, 6 (2) : 267-287. doi: 10.3934/ipi.2012.6.267
[11]

Tianxiao Wang. Characterizations of equilibrium controls in time inconsistent mean-field stochastic linear quadratic problems. I. Mathematical Control & Related Fields, 2019, 9 (2) : 385-409. doi: 10.3934/mcrf.2019018
[12]

Sari Lasanen. Non-Gaussian statistical inverse problems. Part I: Posterior distributions. Inverse Problems & Imaging, 2012, 6 (2) : 215-266. doi: 10.3934/ipi.2012.6.215
[13]

Nobuyuki Kenmochi, Noriaki Yamazaki. Global attractor of the multivalued semigroup associated with a phase-field model of grain boundary motion with constraint. Conference Publications, 2011, 2011 (Special) : 824-833. doi: 10.3934/proc.2011.2011.824
[14]

Jacson Simsen, Mariza Stefanello Simsen, José Valero. Convergence of nonautonomous multivalued problems with large diffusion to ordinary differential inclusions. Communications on Pure & Applied Analysis, 2020, 19 (4) : 2347-2368. doi: 10.3934/cpaa.2020102
[15]

Olexiy V. Kapustyan, Pavlo O. Kasyanov, José Valero, Mikhail Z. Zgurovsky. Attractors of multivalued semi-flows generated by solutions of optimal control problems. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 1229-1242. doi: 10.3934/dcdsb.2019013
[16]

Francesca Papalini. Strongly nonlinear multivalued systems involving singular $\Phi$-Laplacian operators. Communications on Pure & Applied Analysis, 2010, 9 (4) : 1025-1040. doi: 10.3934/cpaa.2010.9.1025
[17]

Raffaela Capitanelli, Salvatore Fragapane. Asymptotics for quasilinear obstacle problems in bad domains. Discrete & Continuous Dynamical Systems - S, 2019, 12 (1) : 43-56. doi: 10.3934/dcdss.2019003
[18]

Frank Hettlich. The domain derivative for semilinear elliptic inverse obstacle problems. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021071
[19]

Abd-semii Oluwatosin-Enitan Owolabi, Timilehin Opeyemi Alakoya, Adeolu Taiwo, Oluwatosin Temitope Mewomo. A new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021004
[20]

Vy Khoi Le. Existence and enclosure of solutions to noncoercive systems of inequalities with multivalued mappings and non-power growths. Discrete & Continuous Dynamical Systems, 2013, 33 (1) : 255-276. doi: 10.3934/dcds.2013.33.255

 Impact Factor: 

Tools

Metrics

  • PDF downloads (41)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy