## Abstract

We consider a mathematical model which describes the quasistatic contact between a viscoelastic body and an obstacle, the so-called foundation. The material’s behavior is modelled with a constitutive law with long memory. The contact is with normal compliance, unilateral constraint, memory effects and adhesion. We present the classical formulation of the problem, then we derive its variational formulation and prove an existence and uniqueness result. The proof is based on arguments of variational inequalities and fixed point.

## Authors

Mircea **Sofonea
**(Laboratoire de Mathématiques et Physique, Université de Perpignan)

Flavius **Patrulescu
**(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

## Keywords

existence, fixed point, mathematical model

## Cite this paper as

M. Sofonea, F. Pătrulescu,* A viscoelastic contact problem with adhesion and surface memory effects*, Math. Model. Anal., vol. 19, no. 5 (2014), pp. 607-626

## About this paper

##### Publisher Name

Vilnius Gediminas Technical University, Vilnius; Taylor & Francis, Abingdon, Oxfordshire

##### DOI

10.3846/13926292.201

##### Print ISSN

1392-6292

##### Online ISSN

1648-3510

## MR

3281333

## ZBL

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