January  2008, 9(1): 129-143. doi: 10.3934/dcdsb.2008.9.129

Noncoercive damping in dynamic hemivariational inequality with application to problem of piezoelectricity

1. 

Department of Mathematics, Central South University, Changsha, Hunan 410076, China

2. 

Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. Nawojki 11, 30-072 Krakow

Received  October 2006 Revised  September 2007 Published  October 2007

In this paper we consider an evolution problem which model the frictional skin effects in piezoelectricity. The model consists of the system of the hemivariational inequality of hyperbolic type for the displacement and the time dependent elliptic equation for the electric potential. In the hemivariational inequality the viscosity term is noncoercive and the friction forces are derived from a nonconvex superpotential through the generalized Clarke subdifferential. The existence of weak solutions is proved by embedding the problem into a class of second order evolution inclusions and by applying a parabolic regularization method.
Citation: Zhenhai Liu, Stanislaw Migórski. Noncoercive damping in dynamic hemivariational inequality with application to problem of piezoelectricity. Discrete & Continuous Dynamical Systems - B, 2008, 9 (1) : 129-143. doi: 10.3934/dcdsb.2008.9.129
[1]

Chibueze Christian Okeke, Abdulmalik Usman Bello, Lateef Olakunle Jolaoso, Kingsley Chimuanya Ukandu. Inertial method for split null point problems with pseudomonotone variational inequality problems. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021037

[2]

Zijia Peng, Cuiming Ma, Zhonghui Liu. Existence for a quasistatic variational-hemivariational inequality. Evolution Equations & Control Theory, 2020, 9 (4) : 1153-1165. doi: 10.3934/eect.2020058

[3]

Stanislaw Migórski. Hemivariational inequality for a frictional contact problem in elasto-piezoelectricity. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1339-1356. doi: 10.3934/dcdsb.2006.6.1339

[4]

Lijing Xi, Yuying Zhou, Yisheng Huang. A class of quasilinear elliptic hemivariational inequality problems on unbounded domains. Journal of Industrial & Management Optimization, 2014, 10 (3) : 827-837. doi: 10.3934/jimo.2014.10.827

[5]

Stanisław Migórski. A note on optimal control problem for a hemivariational inequality modeling fluid flow. Conference Publications, 2013, 2013 (special) : 545-554. doi: 10.3934/proc.2013.2013.545

[6]

Changjie Fang, Weimin Han. Stability analysis and optimal control of a stationary Stokes hemivariational inequality. Evolution Equations & Control Theory, 2020, 9 (4) : 995-1008. doi: 10.3934/eect.2020046

[7]

Leszek Gasiński. Optimal control problem of Bolza-type for evolution hemivariational inequality. Conference Publications, 2003, 2003 (Special) : 320-326. doi: 10.3934/proc.2003.2003.320

[8]

Changjie Fang, Weimin Han. Well-posedness and optimal control of a hemivariational inequality for nonstationary Stokes fluid flow. Discrete & Continuous Dynamical Systems, 2016, 36 (10) : 5369-5386. doi: 10.3934/dcds.2016036

[9]

Aowen Kong, Carlos Nonato, Wenjun Liu, Manoel Jeremias dos Santos, Carlos Raposo. Equivalence between exponential stabilization and observability inequality for magnetic effected piezoelectric beams with time-varying delay and time-dependent weights. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021168

[10]

Leszek Gasiński, Liliana Klimczak, Nikolaos S. Papageorgiou. Nonlinear noncoercive Neumann problems. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1107-1123. doi: 10.3934/cpaa.2016.15.1107

[11]

Vicenţiu D. Rădulescu. Noncoercive elliptic equations with subcritical growth. Discrete & Continuous Dynamical Systems - S, 2012, 5 (4) : 857-864. doi: 10.3934/dcdss.2012.5.857

[12]

Giovanni Cimatti. Forced periodic solutions for piezoelectric crystals. Communications on Pure & Applied Analysis, 2005, 4 (2) : 475-485. doi: 10.3934/cpaa.2005.4.475

[13]

Xin Zuo, Chun-Rong Chen, Hong-Zhi Wei. Solution continuity of parametric generalized vector equilibrium problems with strictly pseudomonotone mappings. Journal of Industrial & Management Optimization, 2017, 13 (1) : 477-488. doi: 10.3934/jimo.2016027

[14]

Maria Michaela Porzio. Existence of solutions for some "noncoercive" parabolic equations. Discrete & Continuous Dynamical Systems, 1999, 5 (3) : 553-568. doi: 10.3934/dcds.1999.5.553

[15]

Masahiro Kubo. Quasi-subdifferential operators and evolution equations. Conference Publications, 2013, 2013 (special) : 447-456. doi: 10.3934/proc.2013.2013.447

[16]

Jianshe Yu, Honghua Bin, Zhiming Guo. Periodic solutions for discrete convex Hamiltonian systems via Clarke duality. Discrete & Continuous Dynamical Systems, 2006, 15 (3) : 939-950. doi: 10.3934/dcds.2006.15.939

[17]

Gabriele Bonanno, Beatrice Di Bella. Fourth-order hemivariational inequalities. Discrete & Continuous Dynamical Systems - S, 2012, 5 (4) : 729-739. doi: 10.3934/dcdss.2012.5.729

[18]

Marius Tucsnak. Control of plate vibrations by means of piezoelectric actuators. Discrete & Continuous Dynamical Systems, 1996, 2 (2) : 281-293. doi: 10.3934/dcds.1996.2.281

[19]

Gustavo Alberto Perla Menzala, Julian Moises Sejje Suárez. On the exponential stabilization of a thermo piezoelectric/piezomagnetic system. Evolution Equations & Control Theory, 2012, 1 (2) : 315-336. doi: 10.3934/eect.2012.1.315

[20]

Gustavo Alberto Perla Menzala, Julian Moises Sejje Suárez. A thermo piezoelectric model: Exponential decay of the total energy. Discrete & Continuous Dynamical Systems, 2013, 33 (11&12) : 5273-5292. doi: 10.3934/dcds.2013.33.5273

2020 Impact Factor: 1.327

Metrics

  • PDF downloads (59)
  • HTML views (0)
  • Cited by (8)

Other articles
by authors

[Back to Top]