Geodesic
A Viscoelastic Frictionless Contact Problem with Adhesion
Arezki Touzaline1
1 Faculté de Mathématiques, USTHB Laboratoire de Systèmes Dynamiques BP 32 El Alia Bab-Ezzouar 16111, Algeria
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) no. 1, pp. 53-66

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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.
DOI : 10.4064/ba63-1-7
Keywords: consider mathematical model which describes equilibrium between viscoelastic body frictionless contact obstacle contact modelled normal compliance associated signorinis conditions adhesion adhesion modelled surface variable bonding field whose evolution described first order differential equation establish variational formulation mechanical problem prove existence uniqueness weak solution proof based arguments evolution equations multivalued maximal monotone operators differential equations banach fixed point theorem

Arezki Touzaline 1

1 Faculté de Mathématiques, USTHB Laboratoire de Systèmes Dynamiques BP 32 El Alia Bab-Ezzouar 16111, Algeria 
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Arezki Touzaline. A Viscoelastic Frictionless Contact Problem with Adhesion. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) no. 1, pp. 53-66. doi: 10.4064/ba63-1-7

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