2007
DOI: 10.1002/mma.957
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Global existence for a contact problem with adhesion

Abstract: SUMMARYIn this paper, we analyze a contact problem with irreversible adhesion between a viscoelastic body and a rigid support. On the basis of Frémond'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 fa… Show more

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Cited by 40 publications
(70 citation statements)
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“…To obtain a contradiction, it is sufficient to extend the approximable solution (u * , χ * ), defined on the interval [0, T * ], to an approximable solution on the interval [0, T * + η] for some η > 0. The argument for this is completely analogous to the one developed in [1,Sec. 5] for the adhesive contact system without nonlocal effects.…”
Section: Local Existence For Problem 22mentioning
confidence: 70%
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“…To obtain a contradiction, it is sufficient to extend the approximable solution (u * , χ * ), defined on the interval [0, T * ], to an approximable solution on the interval [0, T * + η] for some η > 0. The argument for this is completely analogous to the one developed in [1,Sec. 5] for the adhesive contact system without nonlocal effects.…”
Section: Local Existence For Problem 22mentioning
confidence: 70%
“…on Γ C × (0, T ). The operators ρ and β will generalize the subdifferentials ∂I (−∞,0] and ∂I [0,1] in (1.20e). On the one hand, the requirement dom( β) ⊂ [0, +∞) guarantees χ ≥ 0 a.e.…”
Section: Setup and Main Resultsmentioning
confidence: 99%
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