Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Singular perturbation approach to an elastic dry friction problem with non-monotone coefficient

Author: Yves Renard
Journal: Quart. Appl. Math. 58 (2000), 303-324
MSC: Primary 74M10; Secondary 34A60, 34E15
DOI: https://doi.org/10.1090/qam/1753401
MathSciNet review: MR1753401
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Abstract: In this paper we study a one-dimensional dynamic model of dry friction with slip velocity dependent coefficient. In many cases, this model has more than one solution. We introduce a perturbed friction condition which allows us to regain the uniqueness of the solution. We show that the perturbed problem's solutions pointwise converge to a particular solution of the initial problem when the perturbation parameter tends to zero. The singular perturbation approach provides the analysis of a criterion used to select a solution of the problem, and suggests a method to study more elaborated dry friction problems.

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DOI: https://doi.org/10.1090/qam/1753401
Article copyright: © Copyright 2000 American Mathematical Society

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