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


S. Migórski,     migorski(at)softlab.ii.uj.edu.pl
    Jagiellonian University, Institute of Computer Science, Nawojki 11, 30-072 Cracow, Poland


Abstract: In this paper 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. 

Published: Applicable Analysis, vol. 84, nr 7 (2005), 669-699.