A Dynamic Frictionless Contact Problem with Adhesion and Damage

Volume 55 / 2007

Mohamed Selmani, Lynda Selmani Bulletin Polish Acad. Sci. Math. 55 (2007), 17-34 MSC: 35L70, 74M15, 74F25, 74H20. DOI: 10.4064/ba55-1-3

Abstract

We consider a dynamic frictionless contact problem for a viscoelastic material with damage. The contact is modeled with normal compliance condition. The adhesion of the contact surfaces is considered and is modeled with a surface variable, the bonding field, whose evolution is described by a first order differential equation. We establish a variational formulation for the problem and prove the existence and uniqueness of the solution. The proofs are based on the theory of evolution equations with monotone operators, a classical existence and uniqueness result for parabolic inequalities, and fixed point arguments.

Authors

  • Mohamed SelmaniDepartment of Mathematics
    University of Setif
    19000 Setif, Algeria
    e-mail
  • Lynda SelmaniDepartment of Mathematics
    University of Setif
    19000 Setif, Algeria
    e-mail

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