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Existence and Uniqueness to a Dynamic Bilateral Frictional Contact Problem in Viscoelasticity

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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.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Institute of Computer Science, Jagiellonian University, ul. Nawojki 11, 30072, Krakow, Poland

    Zdzisław Denkowski, Stanisław Migórski & Anna Ochal

Authors
  1. Zdzisław Denkowski
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  2. Stanisław Migórski
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  3. Anna Ochal
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Corresponding author

Correspondence to Stanisław Migórski.

Additional information

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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Denkowski, Z., Migórski, S. & Ochal, A. Existence and Uniqueness to a Dynamic Bilateral Frictional Contact Problem in Viscoelasticity. Acta Appl Math 94, 251–276 (2006). https://doi.org/10.1007/s10440-006-9079-5

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  • DOI: https://doi.org/10.1007/s10440-006-9079-5

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