American Institute of Mathematical Sciences

Advanced
2007, 2007(Special): 614-623. doi: 10.3934/proc.2007.2007.614

Periodic stability of elliptic-parabolic variational inequalities with time-dependent boundary double obstacles

Masahiro Kubo 1, and  Noriaki Yamazaki 2,

1. 

Department of Mathematics, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555
2. 

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

Received  September 2006 Revised  January 2007 Published  September 2007

We consider periodic problems of elliptic-parabolic variational inequalities with time-dependent boundary double obstacles. In this paper we assume that the given boundary obstacles change periodically in time. Then, we prove the existence, uniqueness and asymptotic stability of a periodic solution to our problem.
Keywords: Periodic stability, elliptic-parabolic variational inequality, boundary constraints..
Mathematics Subject Classification: 35B10, 35B40, 35J60, 35K55, 35M1.
Citation: Masahiro Kubo, Noriaki Yamazaki. Periodic stability of elliptic-parabolic variational inequalities with time-dependent boundary double obstacles. Conference Publications, 2007, 2007 (Special) : 614-623. doi: 10.3934/proc.2007.2007.614
[1]

Masahiro Kubo, Noriaki Yamazaki. Elliptic-parabolic variational inequalities with time-dependent constraints. Discrete & Continuous Dynamical Systems, 2007, 19 (2) : 335-359. doi: 10.3934/dcds.2007.19.335
[2]

T. A. Shaposhnikova, M. N. Zubova. Homogenization problem for a parabolic variational inequality with constraints on subsets situated on the boundary of the domain. Networks & Heterogeneous Media, 2008, 3 (3) : 675-689. doi: 10.3934/nhm.2008.3.675
[3]

Fabio Paronetto. A Harnack type inequality and a maximum principle for an elliptic-parabolic and forward-backward parabolic De Giorgi class. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 853-866. doi: 10.3934/dcdss.2017043
[4]

Paul Sacks, Mahamadi Warma. Semi-linear elliptic and elliptic-parabolic equations with Wentzell boundary conditions and $L^1$-data. Discrete & Continuous Dynamical Systems, 2014, 34 (2) : 761-787. doi: 10.3934/dcds.2014.34.761
[5]

Noriaki Yamazaki. Doubly nonlinear evolution equations associated with elliptic-parabolic free boundary problems. Conference Publications, 2005, 2005 (Special) : 920-929. doi: 10.3934/proc.2005.2005.920
[6]

J. F. Padial. Existence and estimate of the location of the free-boundary for a non local inverse elliptic-parabolic problem arising in nuclear fusion. Conference Publications, 2011, 2011 (Special) : 1176-1185. doi: 10.3934/proc.2011.2011.1176
[7]

S. J. Li, Z. M. Fang. On the stability of a dual weak vector variational inequality problem. Journal of Industrial & Management Optimization, 2008, 4 (1) : 155-165. doi: 10.3934/jimo.2008.4.155
[8]

Wenyan Zhang, Shu Xu, Shengji Li, Xuexiang Huang. Generalized weak sharp minima of variational inequality problems with functional constraints. Journal of Industrial & Management Optimization, 2013, 9 (3) : 621-630. doi: 10.3934/jimo.2013.9.621
[9]

Shuang Chen, Li-Ping Pang, Dan Li. An inexact semismooth Newton method for variational inequality with symmetric cone constraints. Journal of Industrial & Management Optimization, 2015, 11 (3) : 733-746. doi: 10.3934/jimo.2015.11.733
[10]

Rong Hu, Ya-Ping Fang, Nan-Jing Huang. Levitin-Polyak well-posedness for variational inequalities and for optimization problems with variational inequality constraints. Journal of Industrial & Management Optimization, 2010, 6 (3) : 465-481. doi: 10.3934/jimo.2010.6.465
[11]

Walter Allegretto, Yanping Lin, Shuqing Ma. On the box method for a non-local parabolic variational inequality. Discrete & Continuous Dynamical Systems - B, 2001, 1 (1) : 71-88. doi: 10.3934/dcdsb.2001.1.71
[12]

Nobuyuki Kenmochi. Parabolic quasi-variational diffusion problems with gradient constraints. Discrete & Continuous Dynamical Systems - S, 2013, 6 (2) : 423-438. doi: 10.3934/dcdss.2013.6.423
[13]

X. X. Huang, Xiaoqi Yang. Levitin-Polyak well-posedness in generalized variational inequality problems with functional constraints. Journal of Industrial & Management Optimization, 2007, 3 (4) : 671-684. doi: 10.3934/jimo.2007.3.671
[14]

Francis Akutsah, Akindele Adebayo Mebawondu, Hammed Anuoluwapo Abass, Ojen Kumar Narain. A self adaptive method for solving a class of bilevel variational inequalities with split variational inequality and composed fixed point problem constraints in Hilbert spaces. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021046
[15]

Jorge A. Becerril, Javier F. Rosenblueth. Necessity for isoperimetric inequality constraints. Discrete & Continuous Dynamical Systems, 2017, 37 (3) : 1129-1158. doi: 10.3934/dcds.2017047
[16]

J.-P. Raymond. Nonlinear boundary control of semilinear parabolic problems with pointwise state constraints. Discrete & Continuous Dynamical Systems, 1997, 3 (3) : 341-370. doi: 10.3934/dcds.1997.3.341
[17]

Pavel Gurevich. Periodic solutions of parabolic problems with hysteresis on the boundary. Discrete & Continuous Dynamical Systems, 2011, 29 (3) : 1041-1083. doi: 10.3934/dcds.2011.29.1041
[18]

Jifeng Chu, Meirong Zhang. Rotation numbers and Lyapunov stability of elliptic periodic solutions. Discrete & Continuous Dynamical Systems, 2008, 21 (4) : 1071-1094. doi: 10.3934/dcds.2008.21.1071
[19]

Andrzej Nowakowski. Variational approach to stability of semilinear wave equation with nonlinear boundary conditions. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2603-2616. doi: 10.3934/dcdsb.2014.19.2603
[20]

Takeshi Fukao. Variational inequality for the Stokes equations with constraint. Conference Publications, 2011, 2011 (Special) : 437-446. doi: 10.3934/proc.2011.2011.437

 Impact Factor: 

Tools

Metrics

  • PDF downloads (37)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy