# A Dynamic Frictionless Contact Problem with Adhesion and Damage

• Volume: 55, Issue: 1, page 17-34
• ISSN: 0239-7269

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## Abstract

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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.

## How to cite

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Mohamed Selmani, and Lynda Selmani. "A Dynamic Frictionless Contact Problem with Adhesion and Damage." Bulletin of the Polish Academy of Sciences. Mathematics 55.1 (2007): 17-34. <http://eudml.org/doc/281014>.

@article{MohamedSelmani2007,
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.},
author = {Mohamed Selmani, Lynda Selmani},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {normal compliance; fixed point; variational formulation; existence; uniqueness; monotone operators; parabolic inequalities},
language = {eng},
number = {1},
pages = {17-34},
title = {A Dynamic Frictionless Contact Problem with Adhesion and Damage},
url = {http://eudml.org/doc/281014},
volume = {55},
year = {2007},
}

TY - JOUR
AU - Mohamed Selmani
AU - Lynda Selmani
TI - A Dynamic Frictionless Contact Problem with Adhesion and Damage
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2007
VL - 55
IS - 1
SP - 17
EP - 34
AB - 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.
LA - eng
KW - normal compliance; fixed point; variational formulation; existence; uniqueness; monotone operators; parabolic inequalities
UR - http://eudml.org/doc/281014
ER -

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