On the parametric elliptical variational-hemivariational inequality problem with applications

Abstract

The goal of this paper is to introduce a new class of parametric elliptical variational-hemivariational inequality problems together with parametric inverse problems. We show the existence of solution for parametric inverse problem and well-posedness of parametric elliptical variational-hemivariationl inequality problems. An implementation in nonlinear elasticity, we address the parametric inverse problem for a parametric frictional unilateral contact problem.

Keywords:

• Parametric elliptical variational-hemivariational inequality problems
• parametric inverse problem
• identification
• contact problems
• friction
• nonlinear elasticity

AMS Mathematics Subject Classifications:

• 47J20
• 47J22
• 49J40
• 49J53
• 49N45
• 74M10
• 74M15
• 90C26

Acknowledgments

The authors are grateful to the anonymous referee for their useful comments and suggestions, which have improved the quality of the paper. All authors read and approved the final manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This first author was supported by the Center for General Education, China Medical University, Taichung, Taiwan. The fourth author was funded by the Ministry of Science and Technology, Taiwan [grant number GN 109-2115-M-037-001].