Calculus of Variations and Geometric Measure Theory
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F. Riva

A continuous dependence result for a dynamic debonding model in dimension one

created by riva on 04 Mar 2019

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Submitted Paper

Inserted: 4 mar 2019
Last Updated: 4 mar 2019

Year: 2019

Abstract:

In this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin film peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griffith's criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to different natural topologies.

Keywords: Thin films, Griffith's criterion, Dynamic debonding, Wave equation in time-dependent domains, Continuous dependence


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