Tykhonov triples and convergence results for hemivariational inequalities

Nonlinear Analysis

Rong Hu¹  Yi-Bin Xiao¹  Mircea Sofonea² 

[1] University of Electronic Science and Technology of China;University of Perpignan Via Domitia;

关键词: Tykhonov triple;    well-posedness;    hemivariational inequality;    contact problem;    unilateral constraint;   

DOI  :  10.15388/namc.2021.26.22429

来源: DOAJ

【 摘 要 】

Consider an abstract Problem P in a metric space (X; d) assumed to have a unique solution u. The aim of this paper is to compare two convergence results u'n → u and u''n → u, both in X, and to construct a relevant example of convergence result un → u such that the two convergences above represent particular cases of this third convergence. To this end, we use the concept of Tykhonov triple. We illustrate the use of this new and nonstandard mathematical tool in the particular case of hemivariational inequalities in reflexive Banach space. This allows us to obtain and to compare various convergence results for such inequalities. We also specify these convergences in the study of a mathematical model, which describes the contact of an elastic body with a foundation and provide the corresponding mechanical interpretations.

【 授权许可】

Unknown