Dynamic hemivariational inequality modeling viscoelastic contact problem with normal damped response and friction

Abstract

In this article we examine an evolution problem, which describes the dynamic contact of a viscoelastic body and a foundation. The contact is modeled by a general normal damped response condition and a friction law, which are nonmonotone, possibly multivalued and have the subdifferential form. First we derive a formulation of the model in the form of a multidimensional hemivariational inequality. Then we establish a priori estimates and we prove the existence of weak solutions by using a surjectivity result for pseudomonotone operators. Finally, we deliver conditions under which the solution of the hemivariational inequality is unique.

Keywords:

• Contact problem
• Hemivariational inequality
• Subdifferential
• Damping
• Nonconvex
• Friction
• Hyperbolic
• Viscoelasticity
• Mathematics Subject Classifications AMS 2000:
• 74M15
• 35L70
• 74H20
• 35L85
• 49J40

Acknowledgement

Research was supported in part by the State Committee for Scientific Research of the Republic of Poland (KBN) under Grants Nos. 2 P03A 003 25 and 4T07A 027 26.

Notes

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Additional information

Notes on contributors

Stanisław Migórski *

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