Dynamic adhesive contact of a membrane
type: Item
instance of: scholarly article
title: Dynamic adhesive contact of a membrane
zbMATH Open document ID: 1423.74672
DOI: 10.4171/ZAA/1395
author: R. S. R. Menike
author: K. L. Kuttler
author: M. Shillor
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2010-02-10T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_abstract.php
review text: Summary: This work presents a dynamic model for adhesive contact between a stretched viscoelastic membrane and a reactive obstacle that lies beneath it. The adhesion is described by a bonding field, and the model allows for failure, that is complete debonding in finite time. It is two-dimensional, but retains the essential mathematical structure of the full three-dimensional model. It is set as a hyperbolic equation for the vibrations of the membrane coupled with a nonlinear ordinary differential equation for the evolution of the bonding field. Existence and uniqueness of regular solutions are established in the case of positive viscosity, and in the case of no viscosity, existence of weak solutions is obtained, while the uniqueness of the solutions remains unresolved.
Mathematics Subject Classification ID: 74M15
Mathematics Subject Classification ID: 74K15
Mathematics Subject Classification ID: 74H20
Mathematics Subject Classification ID: 74H25
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 35L85
zbMATH DE Number: 5668455
zbMATH Keywords: dynamic contact
zbMATH Keywords: existence
zbMATH Keywords: deformable obstacle
zbMATH Keywords: membrane
zbMATH Keywords: adhesion
zbMATH Keywords: hyperbolic variational inequality
MaRDI profile type: Publication
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OpenAlex ID: W2009511124
description: scientific article; zbMATH DE number 5668455