Existence and Uniqueness to a Dynamic Bilateral Frictional Contact Problem in Viscoelasticity |
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Authors: | Zdzisław Denkowski Stanisław Migórski Anna Ochal |
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Affiliation: | (1) Faculty of Mathematics and Computer Science, Institute of Computer Science, Jagiellonian University, ul. Nawojki 11, 30072 Krakow, Poland |
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Abstract: | In this paper we examine an evolution problem which describes the dynamic bilateral contact of a viscoelastic body and a foundation. The contact is modeled by a friction multivalued subdifferential boundary condition which incorporates the Coulomb law of friction, the SJK model and the orthotropic friction law. The main result concerns the existence and uniqueness of weak solutions to the hyperbolic variational inequality when the friction coefficient is sufficiently small. The proof is based on a surjectivity result for multivalued operators and a fixed point argument. Research supported in part by the State Committee for Scientific Research of the Republic of Poland (KBN) under Grants no. 2 P03A 003 25 and 4 T07A 027 26. |
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Keywords: | contact problem variational inequality subdifferential Coulomb law friction hyperbolic viscoelasticity evolution inclusion |
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