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Global existence for a contact problem with adhesion

✍ Scribed by Elena Bonetti; Giovanna Bonfanti; Riccarda Rossi

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
308 KB
Volume
31
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

In this paper, we analyze a contact problem with irreversible adhesion between a viscoelastic body and a rigid support. On the basis of FrΓ©mond's theory, we detail the derivation of the model and of the resulting partial differential equation system. Hence, we prove the existence of global in time solutions (to a suitable variational formulation) of the related Cauchy problem by means of an approximation procedure, combined with monotonicity and compactness tools, and with a prolongation argument. In fact the approximate problem (for which we prove a local well‐posedness result) models a contact phenomenon in which the occurrence of repulsive dynamics is allowed for. We also show local uniqueness of the solutions, and a continuous dependence result under some additional assumptions. Copyright Β© 2007 John Wiley & Sons, Ltd.

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## Abstract In this paper the nonlinear viscoelastic wave equation in canonical form equation image with Dirichlet boundary condition is considered. By introducing a new functional and using the potential well method, we show that the damping induced by the viscoelastic term is enough to ensure g