American Institute of Mathematical Sciences

March  2008, 1(1): 117-126. doi: 10.3934/dcdss.2008.1.117

A class of hemivariational inequalities for electroelastic contact problems with slip dependent friction

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

Received  July 2006 Revised  September 2007 Published  December 2007

In this paper we deal with a class of inequality problems for static frictional contact between a piezoelastic body and a foundation. The constitutive law is assumed to be electrostatic and involves a nonlinear elasticity operator. The friction condition is described by the Clarke subdifferential relations of nonmonotone and multivalued character in the tangential directions on the boundary. We derive a variational formulation which is a coupled system of a hemivariational inequality and an elliptic equation. The existence of solutions to the model is a consequence of a more general result obtained from the theory of pseudomonotone mappings.
Citation: Stanislaw Migórski. A class of hemivariational inequalities for electroelastic contact problems with slip dependent friction. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 117-126. doi: 10.3934/dcdss.2008.1.117
 [1] 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 [2] Stanislaw Migórski, Anna Ochal, Mircea Sofonea. Analysis of a dynamic Elastic-Viscoplastic contact problem with friction. Discrete & Continuous Dynamical Systems - B, 2008, 10 (4) : 887-902. doi: 10.3934/dcdsb.2008.10.887 [3] 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 [4] 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 [5] 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 [6] Patrick Ballard. Can the 'stick-slip' phenomenon be explained by a bifurcation in the steady sliding frictional contact problem?. Discrete & Continuous Dynamical Systems - S, 2016, 9 (2) : 363-381. doi: 10.3934/dcdss.2016001 [7] Géry de Saxcé. Modelling contact with isotropic and anisotropic friction by the bipotential approach. Discrete & Continuous Dynamical Systems - S, 2016, 9 (2) : 409-425. doi: 10.3934/dcdss.2016004 [8] Samir Adly, Oanh Chau, Mohamed Rochdi. Solvability of a class of thermal dynamical contact problems with subdifferential conditions. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 91-104. doi: 10.3934/naco.2012.2.91 [9] Alain Léger, Elaine Pratt. On the equilibria and qualitative dynamics of a forced nonlinear oscillator with contact and friction. Discrete & Continuous Dynamical Systems - S, 2016, 9 (2) : 501-527. doi: 10.3934/dcdss.2016009 [10] 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 [11] David Yang Gao. Sufficient conditions and perfect duality in nonconvex minimization with inequality constraints. Journal of Industrial & Management Optimization, 2005, 1 (1) : 53-63. doi: 10.3934/jimo.2005.1.53 [12] Changjie Fang, Weimin Han. Well-posedness and optimal control of a hemivariational inequality for nonstationary Stokes fluid flow. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5369-5386. doi: 10.3934/dcds.2016036 [13] Amina Amassad, Mircea Sofonea. Analysis of a quasistatic viscoplastic problem involving tresca friction law. Discrete & Continuous Dynamical Systems - A, 1998, 4 (1) : 55-72. doi: 10.3934/dcds.1998.4.55 [14] Piotr Kowalski. The existence of a solution for Dirichlet boundary value problem for a Duffing type differential inclusion. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2569-2580. doi: 10.3934/dcdsb.2014.19.2569 [15] Abderrahmane Habbal, Moez Kallel, Marwa Ouni. Nash strategies for the inverse inclusion Cauchy-Stokes problem. Inverse Problems & Imaging, 2019, 13 (4) : 827-862. doi: 10.3934/ipi.2019038 [16] Andaluzia Matei, Mircea Sofonea. Dual formulation of a viscoplastic contact problem with unilateral constraint. Discrete & Continuous Dynamical Systems - S, 2013, 6 (6) : 1587-1598. doi: 10.3934/dcdss.2013.6.1587 [17] Jaroslav Haslinger, Raino A. E. Mäkinen, Jan Stebel. Shape optimization for Stokes problem with threshold slip boundary conditions. Discrete & Continuous Dynamical Systems - S, 2017, 10 (6) : 1281-1301. doi: 10.3934/dcdss.2017069 [18] W. G. Litvinov. Problem on stationary flow of electrorheological fluids at the generalized conditions of slip on the boundary. Communications on Pure & Applied Analysis, 2007, 6 (1) : 247-277. doi: 10.3934/cpaa.2007.6.247 [19] Boris Muha, Zvonimir Tutek. Note on evolutionary free piston problem for Stokes equations with slip boundary conditions. Communications on Pure & Applied Analysis, 2014, 13 (4) : 1629-1639. doi: 10.3934/cpaa.2014.13.1629 [20] Wancheng Sheng, Tong Zhang. Structural stability of solutions to the Riemann problem for a scalar nonconvex CJ combustion model. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 651-667. doi: 10.3934/dcds.2009.25.651

2018 Impact Factor: 0.545