Liu, Zhenhai; Sofonea, Mircea; Xiao, Yi-Bin Tykhonov well-posedness of a frictionless unilateral contact problem. (English) Zbl 1482.74126 Math. Mech. Solids 25, No. 6, 1294-1311 (2020). Summary: We consider a frictionless contact problem, Problem \(\mathcal{P}\), for elastic materials. The process is assumed to be static and the contact is modelled with unilateral constraints. We list the assumptions on the data and derive a variational formulation of the problem, Problem \(\mathcal{P}_V\). Then we consider a perturbation of Problem \(\mathcal{P} \), which could be frictional, governed by a small parameter \(\varepsilon\). This perturbation leads in a natural way to a family of sets \(\{\Omega (\varepsilon)\}_{\varepsilon > 0}\). We prove that Problem \(\mathcal{P}_V\) is well-posed in the sense of Tikhonov with respect to the family \(\{\Omega (\varepsilon)\}_{\varepsilon > 0}\). The proof is based on arguments of monotonicity, pseudomonotonicity and various estimates. We extend these results to a time-dependent version of Problem \(\mathcal{P}\). Finally, we provide examples and mechanical interpretation of our well-posedness results, which, in particular, allow us to establish the link between the weak solutions of different contact models. Cited in 3 Documents MSC: 74M15 Contact in solid mechanics 35Q74 PDEs in connection with mechanics of deformable solids 49J40 Variational inequalities Keywords:contact problem; unilateral constraint; variational inequality; weak solution; Tikhonov well-posedness; approximating sequence; convergence; pseudomonotonicity PDFBibTeX XMLCite \textit{Z. Liu} et al., Math. Mech. Solids 25, No. 6, 1294--1311 (2020; Zbl 1482.74126) Full Text: DOI References: [1] Capatina, A. Variational inequalities and frictional contact problems (Advances in Mechanics and Mathematics, vol. 31). New York: Springer, 2014. · Zbl 1405.49001 [2] Duvaut, G, Lions, JL. Inequalities in mechanics and physics. 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