Some equivalence results for well-posedness of hemivariational inequalities

2014 ◽  
Vol 61 (4) ◽  
pp. 789-802 ◽  
Author(s):  
Yi-bin Xiao ◽  
Xinmin Yang ◽  
Nan-jing Huang
Keyword(s):  
Hemivariational Inequalities ◽  
Well Posedness

A Tykhonov-type well-posedness concept for elliptic hemivariational inequalities

2020 ◽  
Vol 71 (4) ◽  
Author(s):  
Rong Hu ◽  
Mircea Sofonea ◽  
Yi-bin Xiao
Keyword(s):  
Hemivariational Inequalities ◽  
Well Posedness

scholarly journals Well-posedness of Hemivariational Inequalities and Inclusion Problems

2011 ◽  
Vol 15 (3) ◽  
pp. 1261-1276 ◽  
Author(s):  
Yi-bin Xiao ◽  
Nan-jing Huang ◽  
Mu-Ming Wong
Keyword(s):  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Inclusion Problems

scholarly journals On the well-posedness of generalized hemivariational inequalities and inclusion problems in Banach spaces

2016 ◽  
Vol 09 (06) ◽  
pp. 3879-3891 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Yeong-Cheng Liou ◽  
Ching-Feng Wen
Keyword(s):  
Banach Spaces ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Inclusion Problems

scholarly journals Partial differential hemivariational inequalities

2018 ◽  
Vol 7 (4) ◽  
pp. 571-586 ◽  
Author(s):  
Zhenhai Liu ◽  
Shengda Zeng ◽  
Dumitru Motreanu
Keyword(s):  
Evolution Equations ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Upper Semicontinuity ◽  
Solution Set ◽  
Hemivariational Inequality ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Partial Differential ◽  
New Class

AbstractThe aim of this paper is to introduce and study a new class of problems called partial differential hemivariational inequalities that combines evolution equations and hemivariational inequalities. First, we introduce the concept of strong well-posedness for mixed variational quasi hemivariational inequalities and establish metric characterizations for it. Then we show the existence of solutions and meaningful properties such as measurability and upper semicontinuity for the solution set of the mixed variational quasi hemivariational inequality associated to the partial differential hemivariational inequality. Relying, on these properties we are able to prove the existence of mild solutions for partial differential hemivariational inequalities. Furthermore, we show the compactness of the set of the corresponding mild trajectories.

Generalized well-posedness results for a class of hemivariational inequalities

2021 ◽  
pp. 125839
Author(s):  
Jinxia Cen ◽  
Chao Min ◽  
Mircea Sofonea ◽  
Shengda Zeng
Keyword(s):  
Hemivariational Inequalities ◽  
Well Posedness

scholarly journals Metric characterizations for well-posedness of split hemivariational inequalities

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Qiao-yuan Shu ◽  
Rong Hu ◽  
Yi-bin Xiao
Keyword(s):  
Hemivariational Inequalities ◽  
Well Posedness

scholarly journals Well-posedness for generalized variational-hemivariational inequalities with perturbations in reflexive banach spaces

2017 ◽  
Vol 48 (4) ◽  
pp. 345-364 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Yung-Yih Lur ◽  
Ching-Feng Wen
Keyword(s):  
Banach Spaces ◽  
Minimization Problem ◽  
Hemivariational Inequality ◽  
Inclusion Problem ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Reflexive Banach Spaces ◽  
Mild Conditions ◽  
Well Posed

In this paper, we consider an extension of well-posedness for a minimization problem to a class of generalized variational-hemivariational inequalities with perturbations in reflexive Banach spaces. We establish some metric characterizations for the $\alpha$-well-posed generalized variational-hemivariational inequality and give some conditions under which the generalized variational-hemivariational inequality is strongly $\alpha$-well-posed in the generalized sense. Under some mild conditions, we also prove the equivalence between the $\alpha$-well-posedness of the generalized variational-hemivariational inequality and the $\alpha$-well-posedness of the corresponding inclusion problem.

scholarly journals Well-posedness analysis of a stationary Navier–Stokes hemivariational inequality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Min Ling ◽  
Weimin Han
Keyword(s):  
Stokes Equations ◽  
Normal Component ◽  
Numerical Algorithms ◽  
Hemivariational Inequality ◽  
Navier Stokes ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Navier Stokes Equations ◽  
Solution Existence And Uniqueness ◽  
Stationary Navier Stokes Equations

AbstractThis paper provides a well-posedness analysis for a hemivariational inequality of the stationary Navier-Stokes equations by arguments of convex minimization and the Banach fixed point. The hemivariational inequality describes a stationary incompressible fluid flow subject to a nonslip boundary condition and a Clarke subdifferential relation between the total pressure and the normal component of the velocity. Auxiliary Stokes hemivariational inequalities that are useful in proving the solution existence and uniqueness of the Navier–Stokes hemivariational inequality are introduced and analyzed. This treatment naturally leads to a convergent iteration method for solving the Navier–Stokes hemivariational inequality through a sequence of Stokes hemivariational inequalities. Equivalent minimization principles are presented for the auxiliary Stokes hemivariational inequalities which will be useful in developing numerical algorithms.

scholarly journals Well-posedness for systems of time-dependent hemivariational inequalities in Banach spaces

2017 ◽  
Vol 10 (08) ◽  
pp. 4318-4336 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Yeong-Cheng Liou ◽  
Jen-Chih Yao ◽  
Yonghong Yao
Keyword(s):  
Banach Spaces ◽  
Time Dependent ◽  
Hemivariational Inequalities ◽  
Well Posedness
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