Browder-Tikhonov regularization for a class of evolution second order hemivariational inequalities

In this paper, we consider a class of evolution second order hemivariational inequalities with non-coercive operators which are assumed to be known approximately. Using the so-called Browder-Tikhonov regularization method, we prove that the regularized evolution hemivariational inequality problem is solvable. We construct a sequence based on the solvability of the regularized evolution hemivariational inequality problem and show that every weak cluster of this sequence is a solution for the evolution second order hemivariational inequality.

[1]  S. Carl,et al.  Nonlinear Differential Equations in Ordered Spaces , 2000 .

[2]  Stanislaw Migórski,et al.  Boundary Hemivariational Inequalities of Hyperbolic Type and Applications , 2005, J. Glob. Optim..

[3]  Dumitru Motreanu,et al.  Nonsmooth Variational Problems and Their Inequalities: Comparison Principles and Applications , 2010 .

[4]  Panagiotis D. Panagiotopoulos,et al.  Hemivariational Inequalities: Applications in Mechanics and Engineering , 1993 .

[5]  E. Zeidler Nonlinear functional analysis and its applications , 1988 .

[6]  Existence and Comparison Results for Quasilinear Evolution Hemivariational Inequalities , 2004 .

[7]  P. D. Panagiotopoulos,et al.  Coercive and semicoercive hemivariational inequalities , 1991 .

[8]  F. Clarke Optimization And Nonsmooth Analysis , 1983 .

[9]  Franco Giannessi,et al.  Regularization of non-coercive quasi variational inequalities , 2000 .

[10]  Dumitru Motreanu,et al.  Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities , 1998 .

[11]  Zhenhai Liu,et al.  Browder-Tikhonov regularization of non-coercive evolution hemivariational inequalities , 2005 .

[12]  Dumitru Motreanu,et al.  Extremal solutions of quasilinear parabolic inclusions with generalized Clarke's gradient , 2003 .

[13]  Zhenhai Liu Some Convergence Results for Evolution Hemivariational Inequalities , 2004, J. Glob. Optim..

[14]  Monotonicity methods for nonlinear evolution equations , 1996 .

[15]  Yi-bin Xiao,et al.  Sub–supersolution method and extremal solutions for higher order quasi-linear elliptic hemi-variational inequalities☆ , 2007 .

[16]  Nikolas S. Papageorgiou,et al.  An introduction to nonlinear analysis , 2003 .

[17]  Stanislaw Migórski,et al.  Existence of Solutions to Evolution Second Order Hemivariational Inequalities with Multivalued Damping , 2003, System Modelling and Optimization.

[18]  A. Ochal Existence results for evolution hemivariational inequalities of second order , 2005 .

[19]  P. D. Panagiotopoulos,et al.  Mathematical Theory of Hemivariational Inequalities and Applications , 1994 .

[20]  Zdzislaw Naniewicz,et al.  Vector Quasi-Hemivariational Inequalities and Discontinuous Elliptic Systems , 2006, J. Glob. Optim..

[21]  Nan-Jing Huang,et al.  Generalized quasi-variational-like hemivariational inequalities , 2008 .