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A Viscoelastic Frictionless Contact Problem with Adhesion

Volume 63 / 2015

Arezki Touzaline Bulletin Polish Acad. Sci. Math. 63 (2015), 53-66 MSC: 47J20, 49J40, 74M15. DOI: 10.4064/ba63-1-7

Abstract

We consider a mathematical model which describes the equilibrium between a viscoelastic body in frictionless contact with an obstacle. The contact is modelled with normal compliance, associated with Signorini's conditions and adhesion. The adhesion is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove the existence and uniqueness of the weak solution. The proof is based on arguments of evolution equations with multivalued maximal monotone operators, differential equations and the Banach fixed point theorem.

Authors

  • Arezki TouzalineFaculté de Mathématiques, USTHB
    Laboratoire de Systèmes Dynamiques
    BP 32 El Alia
    Bab-Ezzouar 16111, Algeria
    e-mail

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