A Continuous Dependence Result for a Dynamic Debonding Model in Dimension One
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In this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional dynamic 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.
Mathematics Subject Classification (2010)35B30 35L05 35Q74 35R35 70F40 74K35
KeywordsThin films dynamic debonding wave equation in time-dependent domains Griffith’s criterion continuous dependence
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The author wishes to thank Prof. Gianni Dal Maso for many helpful discussions on the topic. The author is a member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).
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